Find palindromic numbers in both binary and ternary bases: Difference between revisions
Find palindromic numbers in both binary and ternary bases (view source)
Revision as of 21:14, 15 April 2024
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{{trans|Python}}
<
F baseN(=num, b)
Line 55:
L(pal23) pal_23(6)
print(pal23‘ ’baseN(pal23, 3)‘ ’baseN(pal23, 2))</
{{out}}
Line 69:
=={{header|Ada}}==
===Simple Technique (Brute Force)===
<
procedure Brute is
Line 95:
end if;
end loop;
end Brute;</
{{out}}
<pre> 0: 0(2), 0(3)
Line 111:
The code is then very fast and also very much readable than if we had done the bit manipulations by hand.
<
procedure Palindromic is
type Int is mod 2**64; -- the size of the unsigned values we will test doesn't exceed 64 bits
Line 159:
end loop;
end loop Process_Each_Power_Of_4;
end Palindromic;</
{{out}}
On a modern machine, (core i5 for example), this code, compiled with the -O3 and -gnatp options, takes less than 5 seconds to give the seven first palindromes smaller than 2^64.
Line 173:
On my machine, this gets the first five results practically instantaneously and the sixth about eight seconds later.
<
script o
property digits : {int mod base as integer}
Line 243:
end task
task()</
{{output}}
<
0 0 0
1 1 1
Line 252:
1422773 101011011010110110101 2200021200022
5415589 10100101010001010100101 101012010210101
90396755477 1010100001100000100010000011000010101 22122022220102222022122"</
=={{header|Arturo}}==
{{trans|Ada}}
<syntaxhighlight lang="rebol">pal2?: function [n][
digs2: digits.base:2 n
return digs2 = reverse digs2
]
revNumber: function [z][
u: z
result: 0
while [u > 0][
result: result + (2*result) + u%3
u: u/3
]
return result
]
pal23: function [][
p3: 1
cnt: 1
print [
pad (to :string 0)++" :" 14
pad.right join to [:string] digits.base:2 0 37 "->"
join to [:string] digits.base:3 0
]
loop 0..31 'p [
while [(p3*(1+3*p3)) < shl 1 2*p]-> p3: p3*3
bound: (shl 1 2*p)/3*p3
limDown: max @[p3/3, bound]
limUp: min @[2*bound, p3-1]
if limUp >= limDown [
loop limDown..limUp 'k [
n: (revNumber k) + (1+3*k)*p3
if pal2? n [
print [
pad (to :string n)++" :" 14
pad.right join to [:string] digits.base:2 n 37 "->"
join to [:string] digits.base:3 n
]
cnt: cnt + 1
if cnt=6 -> return null
]
]
]
]
]
pal23</syntaxhighlight>
{{out}}
<pre> 0 : 0 -> 0
1 : 1 -> 1
6643 : 1100111110011 -> 100010001
1422773 : 101011011010110110101 -> 2200021200022
5415589 : 10100101010001010100101 -> 101012010210101
90396755477 : 1010100001100000100010000011000010101 -> 22122022220102222022122</pre>
=={{header|C}}==
Per the observations made by the Ruby code (which are correct), the numbers must have odd number of digits in base 3 with a 1 at the middle, and must have odd number of digits in base 2.
<
typedef unsigned long long xint;
Line 337 ⟶ 396:
}
return 0;
}</
{{out}}
<pre>0 0(2) 0(3)
Line 347 ⟶ 406:
381920985378904469 10101001100110110110001110011011001110001101101100110010101(2) 2112200222001222121212221002220022112(3)</pre>
=={{header|C sharp|C#}}==
{{works with|C sharp|3}}
No strings involved. Ternary numbers (only of odd length and with a 1 in the middle) are generated by permutating powers of 3<br/>
and then checked to see if they are palindromic in binary.<br/>
The first 6 numbers take about 1/10th of a second. The 7th number takes about 3 and a half minutes.
<
using System.Collections.Generic;
using System.Linq;
Line 434 ⟶ 493:
}
}</
{{out}}
<pre style="height:30ex;overflow:scroll">
Line 460 ⟶ 519:
Ternary: 22122022220102222022122
Binary: 1010100001100000100010000011000010101
</pre>
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <algorithm>
#include <cstdint>
#include <iostream>
// Convert the given decimal number to the given number base
// and return it converted to a string
std::string to_base_string(const uint64_t& number, const uint32_t& base) {
uint64_t n = number;
if ( n == 0 ) {
return "0";
}
std::string result;
while ( n > 0 ) {
result += std::to_string(n % base);
n /= base;
}
std::reverse(result.begin(), result.end());
return result;
}
void display(const uint64_t& number) {
std::cout << "Decimal: " << number << std::endl;
std::cout << "Binary : " << to_base_string(number, 2) << std::endl;
std::cout << "Ternary: " << to_base_string(number, 3) << std::endl << std::endl;
}
bool is_palindromic(const std::string& number) {
std::string copy = number;
std::reverse(copy.begin(), copy.end());
return number == copy;
}
// Create a ternary palindrome whose left part is the ternary equivalent of the given number
// and return it converted to a decimal
uint64_t create_ternary_palindrome(const uint64_t& number) {
std::string ternary = to_base_string(number, 3);
uint64_t power_of_3 = 1;
uint64_t result = 0;
for ( uint64_t i = 0; i < ternary.length(); ++i ) { // Right part of palindrome is the mirror image of left part
if ( ternary[i] > '0' ) {
result += ( ternary[i] - '0' ) * power_of_3;
}
power_of_3 *= 3;
}
result += power_of_3; // Middle digit must be 1
power_of_3 *= 3;
result += number * power_of_3; // Left part is the given number multiplied by the appropriate power of 3
return result;
}
int main() {
std::cout << "The first 6 numbers which are palindromic in both binary and ternary are:" << std::endl;
display(0); // 0 is a palindrome in all 3 bases
display(1); // 1 is a palindrome in all 3 bases
uint64_t number = 1;
uint32_t count = 2;
do {
uint64_t ternary = create_ternary_palindrome(number);
if ( ternary % 2 == 1 ) { // Cannot be an even number since its binary equivalent would end in zero
std::string binary = to_base_string(ternary, 2);
if ( binary.length() % 2 == 1 ) { // Binary palindrome must have an odd number of digits
if ( is_palindromic(binary) ) {
display(ternary);
count++;
}
}
}
number++;
}
while ( count < 6 );
}
</syntaxhighlight>
{{ out }}
<pre>
The first 6 numbers which are palindromic in both binary and ternary are:
Decimal: 0
Binary : 0
Ternary: 0
Decimal: 1
Binary : 1
Ternary: 1
Decimal: 6643
Binary : 1100111110011
Ternary: 100010001
Decimal: 1422773
Binary : 101011011010110110101
Ternary: 2200021200022
Decimal: 5415589
Binary : 10100101010001010100101
Ternary: 101012010210101
Decimal: 90396755477
Binary : 1010100001100000100010000011000010101
Ternary: 22122022220102222022122
</pre>
=={{header|Common Lisp}}==
Unoptimized version
<
(string-equal str (reverse str)) )
Line 475 ⟶ 639:
(palindromep (format nil "~3R" i)) )
(format t "n:~a~:* [2]:~B~:* [3]:~3R~%" i)
(incf results) ))</
{{out}}
<pre>n:0 [2]:0 [3]:0
Line 487 ⟶ 651:
=={{header|D}}==
{{trans|C}}
<
bool isPalindrome2(ulong n) pure nothrow @nogc @safe {
Line 545 ⟶ 709:
}
}
}</
{{out}}
<pre>0 0(3) 0(2)
Line 553 ⟶ 717:
5415589 101012010210101(3) 10100101010001010100101(2)
90396755477 22122022220102222022122(3) 1010100001100000100010000011000010101(2)</pre>
=={{header|EasyLang}}==
<syntaxhighlight>
fastfunc ispalin2 n .
m = n
while m > 0
x = x * 2 + m mod 2
m = m div 2
.
if n = x
return 1
.
.
fastfunc reverse3 n .
while n > 0
r = r * 3 + n mod 3
n = n div 3
.
return r
.
func$ itoa n b .
if n > 0
return itoa (n div b) b & n mod b
.
.
proc main . .
print "0 0(2) 0(3)"
print "1 1(2) 1(3)"
pow3 = 3
while 1 = 1
for i = pow3 / 3 to pow3 - 1
# assumption that the middle digit must be 1
n = (i * 3 + 1) * pow3 + reverse3 i
if ispalin2 n = 1
print n & " " & itoa n 2 & "(2) " & itoa n 3 & "(3)"
cnt += 1
if cnt = 6 - 2
return
.
.
.
pow3 *= 3
.
.
main
</syntaxhighlight>
{{out}}
<pre>
0 0(2) 0(3)
1 1(2) 1(3)
6643 1100111110011(2) 100010001(3)
1422773 101011011010110110101(2) 2200021200022(3)
5415589 10100101010001010100101(2) 101012010210101(3)
90396755477 1010100001100000100010000011000010101(2) 22122022220102222022122(3)
</pre>
=={{header|Elixir}}==
{{trans|Ruby}}
{{works with|Elixir|1.3}}
<
import Integer, only: [is_odd: 1]
Line 584 ⟶ 803:
end
Palindromic.task</
{{out}}
<pre> decimal ternary binary
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=={{header|F_Sharp|F#}}==
<
// Find palindromic numbers in both binary and ternary bases. December 19th., 2018
let fG(n,g)=(Seq.unfold(fun(g,e)->if e<1L then None else Some((g%3L)*e,(g/3L,e/3L)))(n,g/3L)|>Seq.sum)+g+n*g*3L
Seq.concat[seq[0L;1L;2L];Seq.unfold(fun(i,e)->Some (fG(i,e),(i+1L,if i=e-1L then e*3L else e)))(1L,3L)]
|>Seq.filter(fun n->let n=System.Convert.ToString(n,2).ToCharArray() in n=Array.rev n)|>Seq.take 6|>Seq.iter (printfn "%d")
</syntaxhighlight>
{{out}}
Finding 6 takes no time.
Line 626 ⟶ 845:
=={{header|Factor}}==
This implementation uses the methods for reducing the search space discussed in the Ruby example.
<
lists.lazy literals math math.parser sequences tools.time ;
IN: rosetta-code.2-3-palindromes
Line 651 ⟶ 870:
] each ;
[ main ] time</
{{out}}
<pre>The first 6 numbers which are palindromic in both binary and ternary:
Line 685 ⟶ 904:
and check if they are also binary palindromes using the optimizations which have been noted in some
of the other language solutions :
<
'converts decimal "n" to its ternary equivalent
Line 757 ⟶ 976:
Print " seconds on i3 @ 2.13 GHz"
Print "Press any key to quit"
Sleep</
{{out}}
<pre>The first 6 numbers which are palindromic in both binary and ternary are :
Line 790 ⟶ 1,009:
{{trans|C}}
On my modest machine (Intel Celeron @1.6ghz) this takes about 30 seconds to produce the 7th palindrome. Curiously, the C version (GCC 5.4.0, -O3) takes about 55 seconds on the same machine. As it's a faithful translation, I have no idea why.
<
import (
Line 890 ⟶ 1,109:
}
}
}</
{{out}}
Line 932 ⟶ 1,151:
=={{header|Haskell}}==
<
import Data.List (transpose, unwords)
import Numeric (readInt, showIntAtBase)
Line 996 ⟶ 1,215:
showBase :: Integer -> Integer -> String
showBase base n = showIntAtBase base intToDigit n []</
{{Out}}
<pre>Decimal Ternary Binary
Line 1,008 ⟶ 1,227:
=={{header|J}}==
'''Solution:'''
<
toBase=: #.inv"0 NB. convert to base(s) in left arg
filterPalinBase=: ] #~ isPalin@toBase/ NB. palindromes for base(s)
Line 1,028 ⟶ 1,247:
end.
y{.res
)</
'''Usage:'''
<
0 1 6643 1422773
10 2 3 showBases find23Palindromes getfirst 6 NB. first 6 binary & ternary palindomes
Line 1,038 ⟶ 1,257:
1422773 101011011010110110101 2200021200022
5415589 10100101010001010100101 101012010210101
90396755477 1010100001100000100010000011000010101 22122022220102222022122</
=={{header|Java}}==
This takes a while to get to the 6th one (I didn't time it precisely, but it was less than 2 hours on an i7)
<
public static boolean isPali(String x){
return x.equals(new StringBuilder(x).reverse().toString());
Line 1,059 ⟶ 1,278:
}
}
}</
{{out}}
<pre>0, 0, 0
Line 1,067 ⟶ 1,286:
5415589, 10100101010001010100101, 101012010210101
90396755477, 1010100001100000100010000011000010101, 22122022220102222022122</pre>
Alternatively, using a simple and efficient algorithm, the first six number are found in less than a second.
<syntaxhighlight lang="java">
public final class FindPalindromicNumbersBases23 {
public static void main(String[] aArgs) {
System.out.println("The first 7 numbers which are palindromic in both binary and ternary are:");
display(0); // 0 is a palindrome in all 3 bases
display(1); // 1 is a palindrome in all 3 bases
long number = 1;
int count = 2;
do {
long ternary = createTernaryPalindrome(number);
if ( ternary % 2 == 1 ) { // Cannot be an even number since its binary equivalent would end in zero
String binary = toBinaryString(ternary);
if ( binary.length() % 2 == 1 ) { // Binary palindrome must have an odd number of digits
if ( isPalindromic(binary) ) {
display(ternary);
count++;
}
}
}
number++;
}
while ( count < 7 );
}
// Create a ternary palindrome whose left part is the ternary equivalent of the given number
// and return its decimal equivalent
private static long createTernaryPalindrome(long aNumber) {
String ternary = toTernaryString(aNumber);
long powerOf3 = 1;
long sum = 0;
for ( int i = 0; i < ternary.length(); i++ ) { // Right part of a palindrome is the mirror image of left part
if ( ternary.charAt(i) > '0' ) {
sum += ( ternary.charAt(i) - '0' ) * powerOf3;
}
powerOf3 *= 3;
}
sum += powerOf3; // Middle digit must be 1
powerOf3 *= 3;
sum += aNumber * powerOf3; // Left part is the given number multiplied by the appropriate power of 3
return sum;
}
private static boolean isPalindromic(String aNumber) {
return aNumber.equals( new StringBuilder(aNumber).reverse().toString() );
}
private static String toTernaryString(long aNumber) {
if ( aNumber == 0 ) {
return "0";
}
StringBuilder result = new StringBuilder();
while ( aNumber > 0 ) {
result.append(aNumber % 3);
aNumber /= 3;
}
return result.reverse().toString();
}
private static String toBinaryString(long aNumber) {
return Long.toBinaryString(aNumber);
}
private static void display(long aNumber) {
System.out.println("Decimal: " + aNumber);
System.out.println("Binary : " + toBinaryString(aNumber));
System.out.println("Ternary: " + toTernaryString(aNumber));
System.out.println();
}
}
</syntaxhighlight>
{{ out }}
<pre>
The first 7 numbers which are palindromic in both binary and ternary are:
Decimal: 0
Binary : 0
Ternary: 0
Decimal: 1
Binary : 1
Ternary: 1
Decimal: 6643
Binary : 1100111110011
Ternary: 100010001
Decimal: 1422773
Binary : 101011011010110110101
Ternary: 2200021200022
Decimal: 5415589
Binary : 10100101010001010100101
Ternary: 101012010210101
Decimal: 90396755477
Binary : 1010100001100000100010000011000010101
Ternary: 22122022220102222022122
Decimal: 381920985378904469
Binary : 10101001100110110110001110011011001110001101101100110010101
Ternary: 2112200222001222121212221002220022112
</pre>
=={{header|JavaScript}}==
===ES6===
{{Trans|Haskell}}
<
'use strict';
Line 1,195 ⟶ 1,521:
)))
.map(unwords));
})();</
{{Out}}
<pre>Decimal Ternary Binary
Line 1,204 ⟶ 1,530:
5415589 101012010210101 10100101010001010100101
90396755477 22122022220102222022122 1010100001100000100010000011000010101 </pre>
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
The C (jq) and Go (gojq) implementations of jq produce correct results for the first 6 numbers,
as shown below.
jq's "number" type lacks the integer arithmetic precision required to compute the next number
in the sequence, and gojq's memory management is not up to the task even on a generously endowed machine.
'''Generic Utilities'''
<syntaxhighlight lang=jq>
# Convert the input integer to a string in the specified base (2 to 36 inclusive)
def convert(base):
def stream:
recurse(if . >= base then ./base|floor else empty end) | . % base ;
[stream] | reverse
| if base < 10 then map(tostring) | join("")
elif base <= 36 then map(if . < 10 then 48 + . else . + 87 end) | implode
else error("base too large")
end;
# integer division using integer operations only
def idivide($i; $j):
($i % $j) as $mod
| ($i - $mod) / $j ;
def idivide($j):
idivide(.; $j);
# If cond then show the result of update before recursing
def iterate(cond; update):
def i: select(cond) | update | (., i);
i;
</syntaxhighlight>
'''The Task'''
<syntaxhighlight lang=jq>
def isPalindrome2:
if (. % 2 == 0) then . == 0
else {x:0, n: .}
| until(.x >= .n;
.x = .x*2 + (.n % 2)
| .n |= idivide(2) )
| .n == .x or .n == (.x|idivide(2))
end;
def reverse3:
{n: ., x: 0}
| until (.n == 0;
.x = .x*3 + (.n % 3)
| .n |= idivide(3) )
| .x;
def show:
"Decimal : \(.)",
"Binary : \(convert(2))",
"Ternary : \(convert(3))",
"";
def task($count):
"The first \($count) numbers which are palindromic in both binary and ternary are:",
(0|show),
({cnt:1, lo:0, hi:1, pow2:1, pow3:1}
| iterate( .cnt < $count;
.emit = null
| .i = .lo
| until (.i >= .hi or .emit;
((.i*3+1)*.pow3 + (.i|reverse3)) as $n
| if $n|isPalindrome2
then .emit = [$n|show]
| .cnt += 1
else .
end
| .i += 1 )
| if .cnt == $count then . # all done
else if .i == .pow3
then .pow3 *= 3
else .pow2 *= 4
end
| .break = false
| until( .break;
until(.pow2 > .pow3; .pow2 *= 4)
| .lo2 = idivide( idivide(.pow2;.pow3) - 1; 3)
| .hi2 = (idivide(idivide(.pow2*2;.pow3)-1;3) + 1)
| .lo3 = (.pow3|idivide(3))
| .hi3 = .pow3
| if .lo2 >= .hi3 then .pow3 *= 3
elif .lo3 >= .hi2 then .pow2 *= 4
else .lo = ([.lo2, .lo3]|max)
| .hi = ([.hi2, .hi3]|min)
| .break = true
end )
end)
| select(.emit).emit[] );
task(6)
</syntaxhighlight>
<pre>
The first 6 numbers which are palindromic in both binary and ternary are:
Decimal : 0
Binary : 0
Ternary : 0
Decimal : 1
Binary : 1
Ternary : 1
Decimal : 6643
Binary : 1100111110011
Ternary : 100010001
Decimal : 1422773
Binary : 101011011010110110101
Ternary : 2200021200022
Decimal : 5415589
Binary : 10100101010001010100101
Ternary : 101012010210101
Decimal : 90396755477
Binary : 1010100001100000100010000011000010101
Ternary : 22122022220102222022122
</pre>
=={{header|Julia}}==
{{trans|C}}
<
prin3online(n) = println(lpad(n, 15), lpad(string(n, base=2), 40), lpad(string(n, base=3), 30))
reversebase3(n) = (x = 0; while n != 0 x = 3x + (n %3); n = div(n, 3); end; x)
Line 1,256 ⟶ 1,704:
printpalindromes(6)
</
<pre>
Number Base 2 Base 3
Line 1,269 ⟶ 1,717:
=={{header|Kotlin}}==
{{trans|FreeBASIC}}
<
/** converts decimal 'n' to its ternary equivalent */
Line 1,340 ⟶ 1,788:
}
while (count < 6)
}</
{{out}}
<pre>The first 6 numbers which are palindromic in both binary and ternary are:
Line 1,369 ⟶ 1,817:
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
Block[{digits},
If[Divisible[n, 3], {},
Line 1,378 ⟶ 1,826:
];
base2PalindromeQ[n_] := IntegerDigits[n, 2] === Reverse[IntegerDigits[n, 2]];
Select[Flatten[palindromify3 /@ Range[1000000]], base2PalindromeQ]</
{{out}}
Line 1,385 ⟶ 1,833:
=={{header|Nim}}==
{{trans|Ada}}
<
#---------------------------------------------------------------------------------------------------
Line 1,461 ⟶ 1,909:
let t0 = cpuTime()
findPal23()
echo fmt"\nTime: {cpuTime() - t0:.2f}s"</
{{out}}
Line 1,475 ⟶ 1,923:
=={{header|PARI/GP}}==
<
my(N=3^n);
forstep(i=N+1,2*N,[1,2],
Line 1,485 ⟶ 1,933:
)
};
print1("0, 1"); for(i=1,11,check(i))</
{{out}}
<pre>0, 1, 6643, 1422773, 5415589, 90396755477</pre>
Line 1,491 ⟶ 1,939:
=={{header|Perl}}==
{{libheader|ntheory}}
<
print "0 0 0\n"; # Hard code the 0 result
Line 1,502 ⟶ 1,950:
# Print results (including base 10) if base-2 palindrome
print fromdigits($b2,2)," $b3 $b2\n" if $b2 eq reverse($b2);
}</
{{out}}
<pre>0 0 0
Line 1,520 ⟶ 1,968:
that turned out noticeably slower.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #000080;font-style:italic;">-- widths and limits for 32/64 bit running (see output below):</span>
<span style="color: #008080;">constant</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">dsize</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">32</span><span style="color: #0000FF;">?{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">23</span><span style="color: #0000FF;">,</span><span style="color: #000000;">37</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}</span>
<span style="color: #0000FF;">:{</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span><span style="color: #000000;">37</span><span style="color: #0000FF;">,</span><span style="color: #000000;">59</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">}),</span>
<span style="color: #000080;font-style:italic;">-- [atoms on 32-bit have only 53 bits of precision, but 7th ^^^^ requires 59]</span>
<span style="color: #000000;">dfmt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%%%dd"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dsize</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- ie "%12d" or "%18d"</span>
<span style="color: #000000;">esc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#1B</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">center</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">space</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">space</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">space</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">show</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %s %s %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">pad_head</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"decimal"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dsize</span><span style="color: #0000FF;">),</span><span style="color: #000000;">center</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"ternary"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w3</span><span style="color: #0000FF;">),</span><span style="color: #000000;">center</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" binary"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w2</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dfmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %s %s %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">center</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w3</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">center</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w2</span><span style="color: #0000FF;">)})</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">progress64</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">pad_head</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dsize</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"--: %s %s %s\r"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">center</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w3</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">center</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w2</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)+</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">/</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"0"</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">from_base</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">*</span><span style="color: #000000;">base</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- helper function, return s mirrored (if f!=0)
-- and as a (decimal) number (if base!=0)
-- all returns from next_palindrome() get fed through here.</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">f</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">f</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">f</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">base</span><span style="color: #0000FF;">?</span><span style="color: #000000;">from_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">):</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">next_palindrome</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- base is 2 or 3
-- s is not usually a palindrome, but derived from one in <5-base>
--
-- all done with very obvious string manipulations, plus a few
-- less obvious optimisations (odd length, middle 1 in base 3).
--
-- example: next_palindrome(2,"10001000100") -> "10001010001"
--</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- optimisation: palindromes must be odd-length
--
<span style="color: #0000FF;">{</span><span style="color: #004080;">string</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- optimisation: base 3 palindromes have '1' in the middle</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">and</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">'1'</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'1'</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">></span><span style="color: #000000;">s</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- 2) can we (just) increment the middle digit?</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">or</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;"><</span><span style="color: #000000;">base</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'0'</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'1'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- 3) can we increment left half (or is it all <base-1>s?)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">f</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">base</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'0'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">l</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span> <span style="color: #000080;font-style:italic;">-- (stay odd)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">l</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- (even->odd)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- 4) well then, next palindrome is longer, 1000..0001-style</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1%s1"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)})</span>
<span style="color: #000080;font-style:italic;">-- optimisation: base 3 palindromes have '1' in the middle</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'1'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p3</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"0"</span> <span style="color: #000080;font-style:italic;">-- palindromes as strings in base 2 and 3</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">n2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- decimal equivalents of the above.</span>
<span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">limit</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n2</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n3</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">show</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">next_palindrome</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">next_palindrome</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">n2</span><span style="color: #0000FF;"><</span><span style="color: #000000;">n3</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">next_palindrome</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">n2</span><span style="color: #0000FF;">></span><span style="color: #000000;">n3</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">next_palindrome</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">progress64</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">elapsed_short</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">get_key</span><span style="color: #0000FF;">(),{</span><span style="color: #008000;">'q'</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'Q'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">esc</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
32 bit:
Line 1,687 ⟶ 2,138:
=== much simpler version ===
(slightly but not alot faster)
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">result</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">result</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">show</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">n2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">n3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">37</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">))/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">p3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">23</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">))/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %12d %s%s%s %s%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">createpalindrome3</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">power3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ternary</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ternary</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ternary</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">power3</span>
<span style="color: #000000;">power3</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">3</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">power3</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">power3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">3</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%16s %15s %30s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"decimal"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ternary"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"binary"</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">show</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">show</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><</span><span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">n3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">createpalindrome3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">n2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n2</span><span style="color: #0000FF;">[$]=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">n2</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">show</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n3</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 1,746 ⟶ 2,200:
=== much faster version ===
Inspired by Scala 😏
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- convert decimal string s to specified base</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">base</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">2</span> <span style="color: #008080;">and</span> <span style="color: #000000;">base</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (>9 as below)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">/</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)+</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span> <span style="color: #000080;font-style:italic;">-- +(r>9)*('A'-'9'-1)</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trim_head</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #000080;font-style:italic;">-- res = reverse(res) -- (if not palindromic!)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">A</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"1"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"6643"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"1422773"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"5415589"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"90396755477"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"381920985378904469"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"1922624336133018996235"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"2004595370006815987563563"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"8022581057533823761829436662099"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"392629621582222667733213907054116073"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"32456836304775204439912231201966254787"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"428027336071597254024922793107218595973"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"1597863243206403857787246920544522912361"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"30412638162199251273509758127730300026189"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"32345684491703244980406880704479906642045"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"24014998963383302600955162866787153652444049"</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">A</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%=145s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">A</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%=145s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">A</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">3</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre style="font-size: 11px">
0
0
Line 1,823 ⟶ 2,274:
2202021211210100110100002202101000110000220121210220000110001012022000010110010121121202022
</pre>
=={{header|Picat}}==
<syntaxhighlight lang="picat">
import sat.
to_num(List, Base, Num) =>
Len = length(List),
Num #= sum([List[I] * Base**(Len-I) : I in 1..Len]).
palindrom(S) =>
N = len(S),
Start :: 1..N, % start at the first non-zero position:
foreach(I in 1..N)
I1 #= max(1, min(N, N-(I-Start))), % I1 is the symmetry index partner of I (if relevant)
element(I1, S, S1), % S1 is the respective digit
I #< Start #=> S[I] #= 0, % skip leading 0´s
I #= Start #=> S[I] #> 0, % Start points to the first non-zero digit
I #>= Start #=> S[I] #= S1 % palindromic symmetry
end.
constrain(Max, B, X) =>
Len = floor(log(Max) / log(B)) + 1, % length of Max in Base B representation
Digits = new_list(Len), Digits :: 0..B-1,
to_num(Digits, B, X), % Digits show the Base B representation of X
palindrom(Digits).
main =>
N = 11, % maximum number of decimal digits for search, can be set freely
Max = 10**N - 1, % maximum number
X :: 2..Max,
constrain(Max, 2, X),
constrain(Max, 3, X),
Pnumbers = solve_all([X]),
foreach([Y] in [[0], [1]] ++ Pnumbers.sort()) % start with 0 and 1, then show solutions > 1
printf("%w %s %s%n", Y, to_radix_string(Y,2), to_radix_string(Y,3))
end.
</syntaxhighlight>
Output:
<pre>0 0 0
1 1 1
6643 1100111110011 100010001
1422773 101011011010110110101 2200021200022
5415589 10100101010001010100101 101012010210101
90396755477 1010100001100000100010000011000010101 22122022220102222022122</pre>
=={{header|PicoLisp}}==
<
(if (=0 N)
(cons N)
Line 1,842 ⟶ 2,336:
(println N (pack B2) (pack B3))
(inc 'I) )
(inc 'N) ) )</
{{out}}
<pre>0 "0" "0"
Line 1,853 ⟶ 2,347:
=={{header|Python}}==
===Imperative===
<
digits = "0123456789abcdefghijklmnopqrstuvwxyz"
Line 1,886 ⟶ 2,380:
for pal23 in islice(pal_23(), 6):
print(pal23, baseN(pal23, 3), baseN(pal23, 2))</
{{out}}
<pre>0 0 0
Line 1,897 ⟶ 2,391:
===Functional===
{{Works with|Python|3.7}}
<
from itertools import (islice)
Line 1,905 ⟶ 2,399:
def palinBoth():
'''Non finite stream of dually palindromic integers.'''
yield
ibt =
yield ibt
while True:
ibt = until(isBoth)(psucc)(psucc(ibt))
yield
Line 1,931 ⟶ 2,425:
s = showBase3(d)
pal = s + '1' + s[::-1]
return
Line 2,071 ⟶ 2,565:
# MAIN ---
if __name__ == '__main__':
main()</
{{Out}}
<pre> Decimal Binary Ternary
Line 2,083 ⟶ 2,577:
=={{header|Racket}}==
<
(require racket/generator)
Line 2,169 ⟶ 2,663:
(map (curryr number->string 2) (for/list ((i 16) (p (in-producer (b-palindromes-generator 2)))) p))
(list "0" "1" "11" "101" "111" "1001" "1111" "10001" "10101" "11011"
"11111" "100001" "101101" "110011" "111111" "1000001")))</
{{out}}
<pre> 1: 0_10 0_3 0_2
Line 2,182 ⟶ 2,676:
Instead of searching for numbers that are palindromes in one base then checking the other, generate palindromic trinary numbers directly, then check to see if they are also binary palindromes (with additional simplifying constraints as noted in other entries). Outputs the list in decimal, binary and trinary.
<syntaxhighlight lang="raku"
my $pal = $p.base(3);
my $n = :3($pal ~ '1' ~ $pal.flip);
Line 2,192 ⟶ 2,686:
}
printf "%d, %s, %s\n", $_, .base(2), .base(3) for palindromes[^6];</
{{out}}
<pre>0, 0, 0
Line 2,218 ⟶ 2,712:
::* convert the decimal numbers to base 3,
::* ensure that the numbers in base 3 are palindromic.
<
digs=50; numeric digits digs /*biggest known B2B3 palindrome: 44 dig*/
parse arg maxHits .; if maxHits=='' then maxHits=6 /*use six as a limit.*/
Line 2,247 ⟶ 2,741:
if hits>2 then if hits//2 then #=#'0'
if hits<maxHits then return /*Not enough palindromes? Keep looking*/
exit /*stick a fork in it, we're all done. */</
{{out|output|text= when using the default input of: <tt> 7 </tt>}}
<pre> [1] 0 (decimal), ternary= 0
Line 2,273 ⟶ 2,767:
===version 2===
This REXX version takes advantage that the palindromic numbers (in both binary and ternary bases) ''seem'' to only have a modulus nine residue of 1, 5, 7, or 8. With this assumption, the following REXX program is about 25% faster.
<
digs=50; numeric digits digs /*biggest known B2B3 palindrome: 44 dig*/
parse arg maxHits .; if maxHits=='' then maxHits=6 /*use six as a limit.*/
Line 2,303 ⟶ 2,797:
if hits>2 then if hits//2 then #=#'0'
if hits<maxHits then return /*Not enough palindromes? Keep looking*/
exit /*stick a fork in it, we're all done. */</
{{out|output|text= is identical to the 1<sup>st</sup> REXX version.}}
=={{header|Ring}}==
<
# Project: Find palindromic numbers in both binary and ternary bases
Line 2,355 ⟶ 2,849:
return 0
ok
</syntaxhighlight>
{{out}}
<pre>
Line 2,380 ⟶ 2,874:
This program constructs base 3 palindromes using the above "rules" and checks if they happen to be binary palindromes.
<
y << 0
y << 1
Line 2,395 ⟶ 2,889:
n = pal23.next
puts "%2d: %12d %s %s" % [i, n, n.to_s(3).center(25), n.to_s(2).center(39)]
end</
{{out}}
<pre> decimal ternary binary
Line 2,408 ⟶ 2,902:
===Functional programmed, (tail) recursive===
{{Out}}Best seen running in your browser either by [https://scalafiddle.io/sf/ZYCqm7p/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/WIL3oAwYSRy4Kl918u13CA Scastie (remote JVM)].
<
import scala.compat.Platform.currentTime
Line 2,445 ⟶ 2,939:
println(s"Successfully completed without errors. [total ${currentTime - executionStartTime} ms]")
}</
===Fastest and high yields (17) solution 😏===
{{Out}}Best seen running in your browser either by [https://scastie.scala-lang.org/en0ZiqDETCuWO6avhTi9YQ Scastie (remote JVM)].
<
object FastPalindrome23 extends App {
Line 2,471 ⟶ 2,965:
println(s"${count} palindromes found.")
}</
{{Out}}
<pre>Decimal : 0 , Central binary digit: 0
Line 2,561 ⟶ 3,055:
=={{header|Scheme}}==
<
(scheme write)
(srfi 1 lists)) ; use 'fold' from SRFI 1
Line 2,612 ⟶ 3,106:
(r-number->string n 3)))
(newline))
(get-series 6))</
{{out}}
Line 2,624 ⟶ 3,118:
=={{header|Sidef}}==
{{trans|Perl}}
<
format.printf("decimal", "ternary", "binary")
format.printf(0, 0, 0)
Line 2,635 ⟶ 3,129:
format.printf(Num(b2, 2), b3, b2)
}
}</
{{out}}
<pre> decimal ternary binary
Line 2,649 ⟶ 3,143:
{{trans|C}}
<
func isPalin2(n: Int) -> Bool {
Line 2,750 ⟶ 3,244:
}
}
}</
{{out}}
Line 2,764 ⟶ 3,258:
=={{header|Tcl}}==
We can use <tt>[format %b]</tt> to format a number as binary, but ternary requires a custom proc:
<
while {$n} {
append r [expr {$n % 3}]
Line 2,771 ⟶ 3,265:
if {![info exists r]} {set r 0}
string reverse $r
}</
Identifying palindromes is simple. This form is O(n) with a large constant factor, but good enough:
<
The naive approach turns out to be very slow:
<
for {set i 0} {$find} {incr i} {
set b [format %b $i]
Line 2,789 ⟶ 3,283:
}
puts [time {task 4}]</
{{out}}
<pre>Palindrome: 0 (0) (0)
Line 2,800 ⟶ 3,294:
We can do much better than that by naively iterating the binary palindromes. This is nice to do in a coroutine:
<
proc 2pals {} {
Line 2,813 ⟶ 3,307:
yield ${a}1$b
}
}</
The binary strings emitted by this generator are not in increasing order, but for this particular task, that turns out to be unimportant.
Our main loop needs only minor changes:
<
coroutine gen apply {{} {yield; 2pals}}
while {$find} {
Line 2,832 ⟶ 3,326:
}
puts [time task]</
This version finds the first 6 in under 4 seconds, which is good enough for the task at hand:
{{out}}
Line 2,846 ⟶ 3,340:
=={{header|VBA}}==
<
'palindromes both in base3 and base2
'using Decimal data type to find number 6 and 7, although slowly
Line 2,979 ⟶ 3,473:
Debug.Print "Completed in"; (Time3 - Time1) / 1000; "seconds"
Application.ScreenUpdating = True
End Sub</
' 0 0 0 0
' 0 1 1 1
Line 2,995 ⟶ 3,489:
{{libheader|Wren-fmt}}
Just the first 6 palindromes as the 7th is too large for Wren to process without resorting to BigInts.
<
var isPalindrome2 = Fn.new { |n|
Line 3,068 ⟶ 3,562:
}
}
}</
{{out}}
Line 3,108 ⟶ 3,602:
{{trans|Ruby}}
VERY slow after six but does find it.
<
Walker.tweak(fcn(ri,r){ // references to loop start and count of palindromes
foreach i in ([ri.value..*]){
Line 3,120 ⟶ 3,614:
}
}.fp(Ref(3),Ref(3))).push(T(1,0),T(2,1)) // seed with first two results
}</
<
println("%2d: %,d == %.3B(3) == %.2B(2)".fmt(idx,n,n,n))
}</
{{out}}
<pre>
|