Rhonda numbers: Difference between revisions
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=={{header|ALGOL 68}}==
<syntaxhighlight lang="algol68">
BEGIN # find some Rhonda numbers: numbers n in base b such that the product #
# of the digits of n is b * the sum of the prime factors of n #
# returns the sum of the prime factors of n #
PROC factor sum = ( INT n )INT:
BEGIN
INT result := 0;
INT v := ABS n;
WHILE v > 1 AND v MOD 2 = 0 DO
result +:= 2;
v OVERAB 2
OD;
FOR f FROM 3 BY 2 WHILE v > 1 DO
WHILE v > 1 AND v MOD f = 0 DO
result +:= f;
v OVERAB f
OD
OD;
result
END # factor sum # ;
# returns the digit product of n in the specified base #
PROC digit product = ( INT n, base )INT:
IF n = 0 THEN 0
ELSE
INT result := 1;
INT v := ABS n;
WHILE v > 0 DO
result *:= v MOD base;
v OVERAB base
OD;
result
FI # digit product # ;
# returns TRUE if n is a Rhonda number in the specified base, #
# FALSE otherwise #
PROC is rhonda = ( INT n, base )BOOL: base * factor sum( n ) = digit product( n, base );
# returns TRUE if n is prime, FALSE otherwise #
PROC is prime = ( INT n )BOOL:
IF n < 3 THEN n = 2
ELIF n MOD 3 = 0 THEN n = 3
ELIF NOT ODD n THEN FALSE
ELSE
INT f := 5;
INT f2 := 25;
INT to next := 24;
BOOL is a prime := TRUE;
WHILE f2 <= n AND is a prime DO
is a prime := n MOD f /= 0;
f +:= 2;
f2 +:= to next;
to next +:= 8
OD;
is a prime
FI # is prime # ;
# returns a string representation of n in the specified base #
PROC to base string = ( INT n, base )STRING:
IF n = 0 THEN "0"
ELSE
INT under 10 = ABS "0";
INT over 9 = ABS "a" - 10;
STRING result := "";
INT v := ABS n;
WHILE v > 0 DO
INT d = v MOD base;
REPR ( d + IF d < 10 THEN under 10 ELSE over 9 FI ) +=: result;
v OVERAB base
OD;
result
FI # to base string # ;
# find the first few Rhonda numbers in non-prime bases 2 .. max base #
INT max rhonda = 10;
INT max base = 16;
FOR base FROM 2 TO max base DO
IF NOT is prime( base ) THEN
print( ( "The first ", whole( max rhonda, 0 )
, " Rhonda numbers in base ", whole( base, 0 )
, ":", newline
)
);
INT r count := 0;
[ 1 : max rhonda ]INT rhonda;
FOR n WHILE r count < max rhonda DO
IF is rhonda( n, base ) THEN
rhonda[ r count +:= 1 ] := n
FI
OD;
print( ( " in base 10:" ) );
FOR i TO max rhonda DO print( ( " ", whole( rhonda[ i ], 0 ) ) ) OD;
print( ( newline ) );
IF base /= 10 THEN
print( ( " in base ", whole( base, -2 ), ":" ) );
FOR i TO max rhonda DO print( ( " ", to base string( rhonda[ i ], base ) ) ) OD;
print( ( newline ) )
FI
FI
OD
END
</syntaxhighlight>
{{out}}
<pre>
The first 10 Rhonda numbers in base 4:
in base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713
in base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221
The first 10 Rhonda numbers in base 6:
in base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992
in base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132
The first 10 Rhonda numbers in base 8:
in base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956
in base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544
The first 10 Rhonda numbers in base 9:
in base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857
in base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376
The first 10 Rhonda numbers in base 10:
in base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985
The first 10 Rhonda numbers in base 12:
in base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849
in base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35
The first 10 Rhonda numbers in base 14:
in base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945
in base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437
The first 10 Rhonda numbers in base 15:
in base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758
in base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8
The first 10 Rhonda numbers in base 16:
in base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070
in base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e
</pre>
=={{header|Arturo}}==
Line 403 ⟶ 533:
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
</pre>
=={{header|FreeBASIC}}==
{{trans|ALGOL 68}}
<syntaxhighlight lang="vbnet">'#include "isprime.bas"
Function FactorSum(n As Uinteger) As Uinteger
Dim As Uinteger result = 0
Dim As Uinteger v = Abs(n)
While v > 1 And v Mod 2 = 0
result += 2
v \= 2
Wend
For f As Uinteger = 3 To v Step 2
While v > 1 And v Mod f = 0
result += f
v \= f
Wend
Next f
Return result
End Function
Function DigitProduct(n As Uinteger, base_ As Uinteger) As Uinteger
If n = 0 Then Return 0
Dim As Uinteger result = 1
Dim As Uinteger v = Abs(n)
While v > 0
result *= v Mod base_
v \= base_
Wend
Return result
End Function
Function isRhonda(n As Uinteger, base_ As Uinteger) As Uinteger
Return base_ * FactorSum(n) = DigitProduct(n, base_)
End Function
Function ToBaseString(n As Uinteger, base_ As Uinteger) As String
If n = 0 Then Return "0"
Dim As Uinteger under10 = Asc("0")
Dim As Uinteger over9 = Asc("a") - 10
Dim As String result = ""
Dim As Uinteger v = Abs(n)
While v > 0
Dim As Uinteger d = v Mod base_
result = Chr(d + Iif(d < 10, under10, over9)) + result
v \= base_
Wend
Return result
End Function
Dim As Uinteger maxRhonda = 10, maxBase = 16
For base_ As Uinteger = 2 To maxBase
If Not isPrime(base_) Then
Print "The first "; maxRhonda; " Rhonda numbers in base "; base_; ":"
Dim As Uinteger rCount = 0
Dim As Uinteger rhonda(1 To maxRhonda)
Dim As Uinteger n = 1
While rCount < maxRhonda
If isRhonda(n, base_) Then
rCount += 1
rhonda(rCount) = n
End If
n += 1
Wend
Print " in base 10: ";
For i As Uinteger = 1 To maxRhonda
Print " "; rhonda(i);
Next i
Print
If base_ <> 10 Then
Print Using " in base ##: "; base_;
For i As Uinteger = 1 To maxRhonda
Print " "; ToBaseString(rhonda(i), base_);
Next i
Print
End If
End If
Next base_
Sleep</syntaxhighlight>
{{out}}
<pre>Same as ALGOL 68 entry.</pre>
=={{header|Go}}==
Line 1,463 ⟶ 1,675:
base 35:{8232,9476,9633,18634,30954,41905,52215,52440,56889,61992,62146,66339,98260,102180,103305}
base 36:{1000,4800,5670,8190,10998,12412,13300,15750,16821,23016,51612,52734,67744,70929,75030}</pre>
=={{header|Nim}}==
<syntaxhighlight lang="Nim">import std/[sequtils, strformat, strutils]
type Base = 2..36
template isEven(n: int): bool = (n and 1) == 0
func isPrime(n: Natural): bool =
## Return true if "n" is prime.
if n < 2: return false
if n.isEven: return n == 2
if n mod 3 == 0: return n == 3
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, 2
return true
func digitProduct(n: Positive; base: Base): int =
## Return the product of digits of "n" in given base.
var n = n.Natural
result = 1
while n != 0:
result *= n mod base
n = n div base
func primeFactorSum(n: Positive): int =
## Return the sum of prime factors of "n".
var n = n.Natural
while n.isEven:
inc result, 2
n = n shr 1
var d = 3
while d * d <= n:
while n mod d == 0:
inc result, d
n = n div d
inc d, 2
if n > 1: inc result, n
func isRhondaNumber(n: Positive; base: Base): bool =
## Return true if "n" is a Rhonda number to given base.
n.digitProduct(base) == base * n.primeFactorSum
const Digits = toSeq('0'..'9') & toSeq('a'..'z')
func toBase(n: Positive; base: Base): string =
## Return the string representation of "n" in given base.
var n = n.Natural
while true:
result.add Digits[n mod base]
n = n div base
if n == 0: break
# Reverse the digits.
for i in 1..(result.len shr 1):
swap result[i - 1], result[^i]
const N = 10
for base in 2..36:
if base.isPrime: continue
echo &"First {N} Rhonda numbers to base {base}:"
var rhondaList: seq[Positive]
var n = 1
var count = 0
while count < N:
if n.isRhondaNumber(base):
rhondaList.add n
inc count
inc n
echo "In base 10: ", rhondaList.join(" ")
echo &"In base {base}: ", rhondaList.mapIt(it.toBase(base)).join(" ")
echo()
</syntaxhighlight>
{{out}}
<pre>First 10 Rhonda numbers to base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221
First 10 Rhonda numbers to base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132
First 10 Rhonda numbers to base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544
First 10 Rhonda numbers to base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376
First 10 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985
First 10 Rhonda numbers to base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35
First 10 Rhonda numbers to base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437
First 10 Rhonda numbers to base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8
First 10 Rhonda numbers to base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e
First 10 Rhonda numbers to base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9
First 10 Rhonda numbers to base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85
First 10 Rhonda numbers to base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7
First 10 Rhonda numbers to base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj
First 10 Rhonda numbers to base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk
First 10 Rhonda numbers to base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55
First 10 Rhonda numbers to base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd
First 10 Rhonda numbers to base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf
First 10 Rhonda numbers to base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67
First 10 Rhonda numbers to base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq
First 10 Rhonda numbers to base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg
First 10 Rhonda numbers to base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml
First 10 Rhonda numbers to base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo
First 10 Rhonda numbers to base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7
First 10 Rhonda numbers to base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc
</pre>
=={{header|PARI/GP}}==
{{trans|Julia}}
<syntaxhighlight lang="PARI/GP">
isRhonda(n, b) =
{
local(mydigits, product, mysum, factors, pairProduct);
mydigits = digits(n, b);
product = vecprod(mydigits);
factors = factor(n);
mysum= 0;
for(i = 1, matsize(factors)[1],
pairProduct = factors[i, 1] * factors[i, 2];
mysum += pairProduct;
);
product == b * mysum;
}
displayrhondas(low, high, nshow) =
{
local(b, n, rhondas, count, basebRhondas);
for(b = low, high,
if(isprime(b), next);
n = 1; rhondas = [];
count = 0;
while(count < nshow,
if(isRhonda(n, b),
rhondas = concat(rhondas, n);
count++;
);
n++;
);
print("First " nshow " Rhondas in base " b ":");
print("In base 10: " rhondas);
basebRhondas = vector(#rhondas, i, (digits(rhondas[i], b)));
print("In base " b ": " basebRhondas);
print("\n");
);
}
displayrhondas(2, 16, 15);
</syntaxhighlight>
{{out}}
<pre style="height:40ex;overflow:scroll;">
First 15 Rhondas in base 4:
In base 10: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902]
In base 4: [[2, 1, 3, 3, 1, 3, 2], [2, 3, 2, 2, 1, 3, 3], [2, 3, 3, 1, 3, 1, 2], [3, 3, 2, 2, 1, 3, 3], [2, 2, 3, 3, 3, 2, 1, 2], [1, 1, 2, 3, 3, 3, 2, 2, 1], [1, 2, 3, 2, 1, 1, 3, 3, 2], [1, 2, 3, 3, 2, 3, 2, 3, 3], [2, 3, 2, 2, 2, 2, 2, 3, 1], [3, 2, 3, 2, 3, 3, 2, 2, 1], [3, 3, 3, 1, 2, 2, 2, 2, 1], [1, 1, 2, 3, 1, 3, 3, 3, 3, 2], [1, 1, 3, 3, 2, 3, 2, 3, 2, 1], [1, 3, 2, 2, 3, 3, 3, 1, 3, 1], [2, 1, 3, 2, 2, 2, 2, 2, 3, 2]]
First 15 Rhondas in base 6:
In base 10: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821]
In base 6: [[3, 5, 4, 3], [4, 4, 3, 3], [2, 5, 3, 5, 3], [4, 1, 4, 5, 3], [5, 2, 3, 3, 2], [5, 3, 4, 5, 2], [1, 5, 3, 5, 3, 2], [2, 2, 4, 3, 3, 2], [4, 3, 1, 3, 5, 4], [4, 4, 3, 1, 3, 2], [5, 1, 3, 5, 4, 3], [5, 2, 2, 2, 5, 3], [1, 1, 4, 3, 2, 5, 2], [1, 2, 2, 3, 2, 2, 4], [1, 2, 4, 1, 5, 5, 3]]
First 15 Rhondas in base 8:
In base 10: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429]
In base 8: [[3, 4, 5, 4], [1, 4, 2, 5, 6], [1, 4, 7, 3, 6], [2, 4, 4, 4, 2], [3, 4, 2, 4, 4], [3, 4, 6, 2, 3], [4, 2, 3, 6, 7], [4, 4, 1, 6, 6], [6, 1, 4, 6, 6], [6, 2, 5, 4, 4], [7, 3, 5, 4, 2], [1, 1, 4, 4, 5, 7], [1, 1, 4, 6, 3, 5], [1, 4, 3, 2, 7, 3], [1, 4, 4, 3, 4, 5]]
First 15 Rhondas in base 9:
In base 10: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944]
In base 9: [[2, 3, 2, 7, 6], [3, 1, 7, 8, 3], [3, 7, 6, 6, 5], [6, 6, 7, 5, 8], [6, 7, 2, 3, 2], [6, 7, 3, 2, 3], [7, 2, 3, 2, 6], [7, 6, 3, 1, 7], [8, 3, 3, 2, 8], [1, 2, 6, 3, 7, 6], [1, 2, 6, 7, 3, 3], [1, 3, 6, 2, 7, 3], [1, 3, 6, 7, 2, 3], [1, 5, 6, 2, 6, 4], [1, 5, 8, 3, 1, 6]]
First 15 Rhondas in base 10:
In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662]
In base 10: [[1, 5, 6, 8], [2, 8, 3, 5], [4, 7, 5, 2], [5, 2, 6, 5], [5, 4, 3, 9], [5, 6, 6, 4], [5, 8, 2, 4], [5, 8, 3, 2], [8, 5, 2, 6], [1, 2, 9, 8, 5], [1, 5, 6, 2, 5], [1, 5, 6, 9, 8], [1, 9, 4, 3, 5], [2, 5, 2, 8, 4], [2, 5, 6, 6, 2]]
First 15 Rhondas in base 12:
In base 10: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264]
In base 12: [[3, 10, 8], [5, 6, 8], [2, 3, 8, 9], [2, 6, 8, 9], [2, 7, 11, 6], [2, 9, 11, 4], [4, 2, 9, 7], [4, 9, 7, 4], [5, 4, 8, 3], [6, 10, 3, 5], [6, 11, 6, 4], [7, 6, 6, 2], [8, 6, 11, 8], [8, 8, 6, 4], [9, 4, 11, 4]]
First 15 Rhondas in base 14:
In base 10: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543]
In base 14: [[4, 2, 7, 9], [6, 11, 2, 7], [7, 6, 12, 13], [10, 11, 2, 7], [11, 7, 12, 1], [1, 2, 7, 7, 13], [1, 7, 3, 13, 10], [1, 7, 5, 4, 7], [1, 7, 11, 12, 2], [1, 9, 4, 3, 7], [1, 10, 8, 7, 3], [1, 11, 1, 7, 10], [2, 5, 3, 7, 7], [2, 8, 4, 2, 7], [3, 3, 10, 7, 5]]
First 15 Rhondas in base 15:
In base 10: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483]
In base 15: [[10, 9, 7], [10, 14, 12], [3, 5, 14, 8], [4, 10, 8, 3], [5, 2, 6, 9], [5, 5, 8, 6], [5, 10, 1, 12], [5, 14, 3, 9], [7, 3, 5, 13], [9, 1, 10, 8], [9, 3, 6, 10], [9, 11, 10, 4], [9, 14, 1, 10], [11, 3, 8, 5], [11, 10, 7, 3]]
First 15 Rhondas in base 16:
In base 10: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465]
In base 16: [[3, 14, 8], [4, 6, 14], [1, 10, 7, 8], [3, 14, 2, 8], [4, 12, 10, 8], [4, 14, 4, 11], [4, 15, 8, 3], [5, 13, 8, 10], [6, 6, 11, 8], [7, 1, 8, 14], [7, 12, 10, 2], [7, 14, 2, 4], [8, 5, 11, 12], [8, 6, 13, 9], [8, 14, 7, 1]]
</pre>
=={{header|Perl}}==
Line 2,222 ⟶ 2,700:
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt, Conv
| |||