Strange numbers
n is a strange number if every adjacent decimal digit differs from its neighbour by a prime number.
Show all strange numbers for 100 < n < 500
- Stretch goal
Show the number of 10-digit strange numbers that begin with 1
11l
<lang 11l>F is_strange(n)
V xs = String(n).map(c -> Int(c)) R all(zip(xs, xs[1..]).map((a, b) -> abs(a - b) C (2, 3, 5, 7)))
V xs = (100..500).filter(n -> is_strange(n)) print("\nStrange numbers in range [100..500]\n") print(‘(Total: ’String(xs.len)")\n") L(el) xs
print(el, end' ‘ ’)
I L.index % 10 == 9
print()</lang>
- Output:
Strange numbers in range [100..500] (Total: 87) 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
ALGOL W
<lang algolw>begin % find "strange numbers" - numbers where digits differ from the next %
% by a prime %
% returns true if n is strange, false otherwise %
logical procedure isStrange( integer value n ) ;
begin
integer rest;
rest := abs( n );
if rest < 10 then false
else begin
logical strange;
integer d0;
strange := true;
d0 := rest rem 10;
rest := rest div 10;
while strange and rest > 0 do begin
integer d1, diff;
d1 := rest rem 10;
rest := rest div 10;
diff := abs( d1 - d0 );
strange := diff = 2 or diff = 3 or diff = 5 or diff = 7;
d0 := d1
end while_strange_and_rest_gt_0 ;
strange
end if_rest_lt_10__
end isStrange ;
% test the isStrange procedure on values 100-499 %
begin
integer strangeCount;
strangeCount := 0;
for n := 100 until 499 do begin;
if isStrange( n ) then begin
strangeCount := strangeCount + 1;
if strangeCount rem 20 = 1
then write( i_w := 4, s_w := 0, n )
else writeon( i_w := 4, s_w := 0, n )
end if_isStrange_n
end for_n
end
end.</lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
APL
<lang APL>(⊢(/⍨)(∧/2 3 5 7∊⍨2+/⍎¨∘⍕)¨) 100+⍳400</lang>
- Output:
111 112 114 116 120 121 123 125 141 143 161 202 203 205 207 211 212 214 216 230 232 234 250 252 302 303 305 307 320 321
323 325 341 343 411 412 414 416 430 432 434
AppleScript
<lang AppleScript>--------------------- STRANGE NUMBERS --------------------
-- isStrange :: Int -> Bool on isStrange(n)
set ds to digits(n)
script sumIsSmallPrime
on |λ|(a, b)
{2, 3, 5, 7} contains abs(a - b)
end |λ|
end script
zipWith(sumIsSmallPrime, ds, rest of ds) ¬
does not contain false
end isStrange
TEST -------------------------
on run
set xs to filter(isStrange, enumFromTo(100, 500))
intercalate("\n\n", ¬
{"Strange numbers found in range [100..500]", ¬
"Full list:", ¬
("(total " & (length of xs) as string) & ")", ¬
unlines(map(unwords, chunksOf(10, map(str, xs))))})
end run
GENERIC ------------------------
-- abs :: Num -> Num on abs(x)
-- Absolute value.
if 0 > x then
-x
else
x
end if
end abs
-- chunksOf :: Int -> [a] -> a
on chunksOf(k, xs)
script
on go(ys)
set ab to splitAt(k, ys)
set a to item 1 of ab
if {} ≠ a then
{a} & go(item 2 of ab)
else
a
end if
end go
end script
result's go(xs)
end chunksOf
-- digits :: Int -> [Int]
on digits(n)
script go
on |λ|(x)
x as integer
end |λ|
end script
map(go, characters of (n as string))
end digits
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
lst
else
{}
end if
end enumFromTo
-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, delim}
set s to xs as text
set my text item delimiters to dlm
s
end intercalate
-- filter :: (a -> Bool) -> [a] -> [a]
on filter(p, xs)
tell mReturn(p)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
if {text, string} contains class of xs then
lst as text
else
lst
end if
end tell
end filter
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f
-- to each element of xs.
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
if n > 0 and n < length of xs then
if class of xs is text then
{items 1 thru n of xs as text, ¬
items (n + 1) thru -1 of xs as text}
else
{items 1 thru n of xs, items (n + 1) thru -1 of xs}
end if
else
if n < 1 then
{{}, xs}
else
{xs, {}}
end if
end if
end splitAt
-- str :: a -> String
on str(x)
x as string
end str
-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set s to xs as text
set my text item delimiters to dlm
s
end unlines
-- unwords :: [String] -> String
on unwords(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, space}
set s to xs as text
set my text item delimiters to dlm
return s
end unwords
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
if 1 > lng then
return {}
else
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end if
end zipWith</lang>
- Output:
Strange numbers found in range [100..500] Full list: (total 87) 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
AWK
<lang AWK>
- syntax: GAWK -f STRANGE_NUMBERS.AWK
BEGIN {
start = 100
stop = 500
for (i=start; i<=stop; i++) {
flag = 1
for (j=1; j<length(i); j++) {
if (!(is_prime(abs(substr(i,j,1)-substr(i,j+1,1))))) {
flag = 0
break
}
}
if (flag == 1) {
printf("%d%1s",i,++count%10?"":"\n")
}
}
printf("\nStrange numbers %d-%d: %d\n",start,stop,count)
exit(0)
} function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
} function abs(x) { if (x >= 0) { return x } else { return -x } } </lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 Strange numbers 100-500: 87
BASIC
<lang basic>10 DEFINT I,J,K: DEFSTR S 20 FOR I=100 TO 500 30 S=STR$(I) 40 FOR J=2 TO LEN(S)-1 50 K=ABS(VAL(MID$(S,J,1))-VAL(MID$(S,J+1,1))) 60 IF K<>2 AND K<>3 AND K<>5 AND K<>7 THEN 90 70 NEXT J 80 PRINT I, 90 NEXT I</lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
BCPL
<lang bcpl>get "libhdr"
let dgtprime(x) = x=2 | x=3 | x=5 | x=7 let strange(x) =
x<10 -> true, dgtprime(abs(x rem 10 - (x/10) rem 10)) & strange(x/10)
let start() be $( let col = 0
for i=100 to 500 do
if strange(i) then
$( writed(i, 4)
col := col + 1
if col rem 10 = 0 then wrch('*N')
$)
wrch('*N')
$)</lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
C
<lang c>#include <stdbool.h>
- include <stdio.h>
bool isPrime(int n) {
if (n < 0) {
n = -n;
}
return n == 2 || n == 3 || n == 5 || n == 7;
}
int main() {
int count = 0; int i, j; int d[3]; int dptr;
printf("Strange numbers in the open interval (100, 500) are:\n");
for (i = 101; i < 500; i++) {
dptr = 0;
j = i;
while (j > 0) {
d[dptr++] = j % 10;
j /= 10;
}
if (isPrime(d[0] - d[1]) && isPrime(d[1] - d[2])) {
printf("%d ", i);
count++;
if (count % 10 == 0) {
printf("\n");
}
}
}
if (count % 10 != 0) {
printf("\n");
}
printf("\n%d strange numbers in all.\n", count);
return 0;
}</lang>
- Output:
Strange numbers in the open interval (100, 500) are: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 87 strange numbers in all.
C++
<lang cpp>#include <algorithm>
- include <iostream>
- include <vector>
std::vector<int> digits(int n) {
std::vector<int> result;
while (n > 0) {
auto rem = n % 10;
result.push_back(rem);
n /= 10;
}
std::reverse(result.begin(), result.end());
return result;
}
bool is_strange(int n) {
auto test = [](int a, int b) {
auto v = std::abs(a - b);
return v == 2 || v == 3 || v == 5 || v == 7;
};
auto xs = digits(n);
for (size_t i = 1; i < xs.size(); i++) {
if (!test(xs[i - 1], xs[i])) {
return false;
}
}
return true;
}
int main() {
std::vector<int> xs;
for (int i = 100; i <= 500; i++) {
if (is_strange(i)) {
xs.push_back(i);
}
}
std::cout << "Strange numbers in range [100..500]\n"; std::cout << "(Total: " << xs.size() << ")\n\n";
for (size_t i = 0; i < xs.size(); i++) {
std::cout << xs[i];
if ((i + 1) % 10 == 0) {
std::cout << '\n';
} else {
std::cout << ' ';
}
}
return 0;
}</lang>
- Output:
Strange numbers in range [100..500] (Total: 87) 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
F#
<lang fsharp> // Strange numbers. Nigel Galloway: February 25th., 2021 let N=Array.init 10(fun n->[2;3;5;7]|>List.collect(fun g->[n+g;n-g])|>List.filter((<) -1)|>List.filter((>)10)) [1..4]|>List.collect(fun g->N.[g]|>List.map(fun n->g*10+n%10))|>List.collect(fun n->N.[n%10]|>List.map(fun g->n*10+g%10))|>List.iter(printf "%d "); printfn "" </lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 180 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 380 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Factor
Identifying and filtering
<lang factor>USING: grouping io kernel math.ranges math.statistics math.text.utils math.vectors prettyprint sequences ;
- strange? ( n -- ? )
1 digit-groups differences vabs
[ { 2 3 5 7 } member? ] all? ;
"Strange numbers in (100, 500):" print nl 100 500 (a,b) [ strange? ] filter dup 10 group [ [ pprint bl ] each nl ] each nl length pprint " strange numbers found." print</lang>
- Output:
Strange numbers in (100, 500): 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 87 strange numbers found.
Generating
Since we know the next possible digits based on the current last digit, we can construct strange numbers with a backtracking algorithm.
<lang factor>USING: backtrack compiler.tree.propagation.call-effect formatting io kernel sequences sequences.generalizations tools.memory.private tools.time ;
- d ( digit -- digit next-digit )
dup {
{ 2 3 5 7 } ! from 0 we can get to these digits
{ 3 4 6 8 } ! from 1 we can get to these
{ 0 4 5 7 9 } ! etc...
{ 0 1 5 6 8 }
{ 1 2 6 7 9 }
{ 0 2 3 7 8 }
{ 1 3 4 8 9 }
{ 0 2 4 5 9 }
{ 1 3 5 6 }
{ 2 4 6 7 }
} nth amb-lazy ;
[ [ 1 d d d d d d d d d 10 narray ] bag-of ] time
dup length commas write " 10-digit strange numbers beginning with 1:" print [ first2 ] [ last2 ] bi "%u\n%u\n...\n%u\n%u\n" printf</lang>
- Output:
Running time: 1.904245898 seconds
853,423 10-digit strange numbers beginning with 1:
{ 1 3 0 2 0 2 0 2 0 2 }
{ 1 3 0 2 0 2 0 2 0 3 }
...
{ 1 8 6 9 7 9 7 9 7 5 }
{ 1 8 6 9 7 9 7 9 7 9 }
FreeBASIC
<lang freebasic>function is_strange( n as ulongint ) as boolean
dim as uinteger d, ld, a if n<10 then return true 'arbitrary, but makes the recursion easier d = n mod 10 ld = (n mod 100) \ 10 a = abs(d - ld) if a = 2 or a = 3 or a = 5 or a = 7 then return is_strange(n\10) else return false
end function
print "Strange numbers between 100 and 500" for n as uinteger = 101 to 499
if is_strange(n) then print n;" ";
next n print : print
dim as integer c = 0 for n as ulongint = 1000000000 to 1999999999
if is_strange(n) then c+=1
next n print using "There are ####### 10-digit strange numbers beginning with 1.";c</lang>
- Output:
Strange numbers between 100 and 500 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
There are 853423 10-digit strange numbers beginning with 1.
Forth
<lang forth>\ tests whether n is prime for 0 <= n < 10
- prime? ( n -- ? )
1 swap lshift 0xac and 0<> ;
- strange? ( n -- ? )
dup 10 < if drop false exit then 10 /mod swap >r begin dup 0 > while 10 /mod swap dup r> - abs prime? invert if 2drop false exit then >r repeat drop rdrop true ;
- main
0
500 101 do
i strange? if
i .
1+
dup 10 mod 0= if cr then else
then
loop
cr
drop ;
main bye</lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Go
Basic task
<lang go>package main
import "fmt"
func isPrime(n int) bool {
if n < 0 {
n = -n
}
return n == 2 || n == 3 || n == 5 || n == 7
}
func main() {
count := 0
var d []int
fmt.Println("Strange numbers in the open interval (100, 500) are:\n")
for i := 101; i < 500; i++ {
d = d[:0]
j := i
for j > 0 {
d = append(d, j%10)
j /= 10
}
if isPrime(d[0]-d[1]) && isPrime(d[1]-d[2]) {
fmt.Printf("%d ", i)
count++
if count%10 == 0 {
fmt.Println()
}
}
}
if count%10 != 0 {
fmt.Println()
}
fmt.Printf("\n%d strange numbers in all.\n", count)
}</lang>
- Output:
Strange numbers in the open interval (100, 500) are: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 87 strange numbers in all.
Stretch goal
<lang go>package main
import "fmt"
func main() {
diffs := []int{-7, -5, -3, -2, 2, 3, 5, 7}
possibles := make([][]int, 10)
for i := 0; i < 10; i++ {
possibles[i] = []int{}
for _, d := range diffs {
sum := i + d
if sum >= 0 && sum < 10 {
possibles[i] = append(possibles[i], sum)
}
}
}
places := 10
start := 1
strangeOnes := []int{start}
for i := 2; i <= places; i++ {
var newOnes []int
for _, n := range strangeOnes {
for _, nextN := range possibles[n%10] {
newOnes = append(newOnes, n*10+nextN)
}
}
strangeOnes = newOnes
}
fmt.Println("Found", len(strangeOnes), places, "\b-digit strange numbers beginning with", start)
}</lang>
- Output:
Found 853423 10-digit strange numbers beginning with 1.
Haskell
<lang haskell>import Data.List (intercalate) import Data.List.Split (chunksOf)
STRANGE NUMBERS --------------------
isStrange :: Int -> Bool isStrange n =
all (\(a, b) -> abs (a - b) `elem` [2, 3, 5, 7]) $ (zip <*> tail) (digits n)
digits :: Int -> [Int] digits = fmap (read . return) . show
TEST -------------------------
main =
let xs = filter isStrange [100 .. 500]
in (putStrLn . intercalate "\n\n")
[ "Strange numbers found in range [100..500]",
"(total " <> (show . length) xs <> ")",
"Full list:",
unlines
(unwords <$> chunksOf 10 (show <$> xs))
]</lang>
- Output:
Strange numbers found in range [100..500] (total 87) Full list: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Java
<lang Java>import java.util.LinkedList; import java.util.List; import java.util.function.BiPredicate; import java.util.stream.Collectors; import java.util.stream.IntStream;
public class StrangeNumbers {
private static List<Integer> digits(int n) {
var result = new LinkedList<Integer>();
while (n > 0) {
var rem = n % 10;
result.addFirst(rem);
n /= 10;
}
return result;
}
private static boolean isStrange(int n) {
BiPredicate<Integer, Integer> test = (a, b) -> {
var abs = Math.abs(a - b);
return abs == 2 || abs == 3 || abs == 5 || abs == 7;
};
var xs = digits(n);
for (int i = 1; i < xs.size(); i++) {
if (test.negate().test(xs.get(i - 1), xs.get(i))) {
return false;
}
}
return true;
}
public static void main(String[] args) {
var xs = IntStream.rangeClosed(100, 500)
.filter(StrangeNumbers::isStrange)
.boxed()
.collect(Collectors.toList());
System.out.println("Strange numbers in range [100..500]");
System.out.printf("(Total: %d)\n\n", xs.size());
for (int i = 0; i < xs.size(); i++) {
Integer x = xs.get(i);
System.out.print(x);
if ((i + 1) % 10 == 0) {
System.out.println();
} else {
System.out.print(' ');
}
}
}
}</lang>
- Output:
Strange numbers in range [100..500] (Total: 87) 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Julia
Filter method
<lang julia>isstrange(n::Integer) = (d = digits(n); all(i -> abs(d[i] - d[i + 1]) ∈ [2, 3, 5, 7], 1:length(d)-1))
function filter_open_interval(start, stop, f, doprint=true, rowlength=92)
colsize = length(string(stop)) + 1
columns, ncount = rowlength ÷ colsize, 0
println("Finding numbers matching $f for open interval ($start, $stop):\n")
for n in start+1:stop-1
if f(n)
ncount += 1
doprint && print(rpad(n, colsize), ncount % columns == 0 ? "\n" : "")
end
end
println("\n\nThe total found was $ncount\n\n")
end
filter_open_interval(100, 500, isstrange)
</lang>
- Output:
Finding numbers matching isstrange for open interval (100, 500): 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 The total found was 87
Generator method
HT: Factor for the table. <lang julia>function countstrange(places, fixedstart=1)
possibles = [
[2, 3, 5, 7],
[3, 4, 6, 8],
[0, 4, 5, 7, 9],
[0, 1, 5, 6, 8],
[1, 2, 6, 7, 9],
[0, 2, 3, 7, 8],
[1, 3, 4, 8, 9],
[0, 2, 4, 5, 9],
[1, 3, 5, 6],
[2, 4, 6, 7],
]
strangeones = [fixedstart]
for _ in 2:places
newones = Int[]
for n in strangeones, nextn in possibles[n % 10 + 1]
push!(newones, n * 10 + nextn)
end
strangeones = newones
end
println("Found ", length(strangeones), " $places-digit strange numbers with the most significant digit $fixedstart.\n")
end
countstrange(10) @time countstrange(10)
</lang>
- Output:
Found 853423 10-digit strange numbers with the most significant digit 1. Found 853423 10-digit strange numbers with the most significant digit 1. 0.014545 seconds (139 allocations: 13.298 MiB, 29.39% gc time)
MAD
<lang MAD> NORMAL MODE IS INTEGER
INTERNAL FUNCTION(D)
ENTRY TO PRMDGT.
DD = D
WHENEVER DD.LE.0, DD=-D
FUNCTION RETURN
0 DD.E.2 .OR. DD.E.3 .OR. DD.E.5 .OR. DD.E.7
END OF FUNCTION
INTERNAL FUNCTION(A,B)
ENTRY TO REM.
FUNCTION RETURN A-A/B*B
END OF FUNCTION
INTERNAL FUNCTION(X)
ENTRY TO STRNGE.
XX = X
LOOP WHENEVER XX.G.9
D0 = REM.(XX,10)
XX = XX/10
D1 = REM.(XX,10)
WHENEVER PRMDGT.(D0-D1), TRANSFER TO LOOP
FUNCTION RETURN 0B
END OF CONDITIONAL
FUNCTION RETURN 1B
END OF FUNCTION
PRINT COMMENT $ STRANGE NUMBERS $
THROUGH TEST, FOR I=100, 1, I.GE.500
TEST WHENEVER STRNGE.(I), PRINT FORMAT F, I
VECTOR VALUES F = $I4*$
END OF PROGRAM </lang>
- Output:
STRANGE NUMBERS 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Pascal
modified recursive version like Julia/Factor using the digits that can follow.
Not dynamically memorizing of all numbers saves much time 200ms -> 4ms.
Count is about 4.6 to the power of Digitscount -> first digit 1 followed by 9 digit -> 4.6^9 = 922190
<lang pascal>program strangenumbers;
const
dgtMaxCnt = 10;
deltaDgtCnt: array[0..9] of Int32 =(4,4,5,5,5,5,5,5,4,4); // (4*4+6*5)/10 => 4.6
// digits that can follow
DPrmNxtDgt : array[0..9,0..4] of Int32 =((2,3,5,7,0), //0 +2,+3,+5,+7
(3,4,6,8,0), //1 +2,+3,+5,+7
(0,4,5,7,9), //2 -2,+2,+3,+5,+7
(0,1,5,6,8), //3 -3,-2,+2,+3,+5
(1,2,6,7,9), //4 -3,-2,+2,+3,+5
(0,2,3,7,8), //5 -5,-3,-2,+2,+3
(1,3,4,8,9), //6 -5,-3,-2,+2,+3
(0,2,4,5,9), //7 -7,-5,-3,-2,+2
(1,3,5,6,0), //8 -7,-5,-3,-2
(2,4,6,7,0)); //9 -7,-5,-3,-2
type
tDigits = array[0..dgtMaxCnt-1] of Int32;
//globals are set to 0 var
Digits : tDigits; i,Cnt,dgtCnt : Int32;
procedure OutPut(const Digits:tDigits); var
i : Int32;
Begin
For i := 0 to dgtcnt-1 do
write(Digits[i]);
write(' ');
end;
procedure NextDigit(var Digits:TDigits;DgtIdx:Int32); var
idx,dgt :Int32;
Begin
dgt := Digits[DgtIdx];
inc(DgtIdx);
IF DgtIdx < dgtCnt-1 then
Begin
For idx := 0 to deltaDgtCnt[dgt]-1 do
Begin
Digits[DgtIdx]:= DPrmNxtDgt[dgt,idx];
NextDigit(Digits,DgtIdx);
end;
end
else
Begin
For idx := 0 to deltaDgtCnt[dgt]-1 do
Begin
Digits[DgtIdx]:= DPrmNxtDgt[dgt,idx];
inc(cnt);
IF dgtCnt<5 then
Begin
OutPut(Digits);
If cnt mod 16 = 0 then
Writeln;
end;
end;
end;
end;
Begin
cnt := 0;
dgtCnt := 3;
Writeln('Count of digits : ', dgtCnt,' in 100..499');
For i := 1 to 4 do
Begin
Digits[0] := i;
NextDigit(Digits,0);
end;
Writeln;
Writeln('Count : ',cnt);
Writeln;
cnt := 0;
dgtCnt := 10;
Writeln('Count of digits : ', dgtCnt);
For i := 1 to 1 do
Begin
Digits[0] := i;
NextDigit(Digits,0);
end;
Writeln;
Writeln('Count : ',cnt);
end.</lang>
- Output:
Count of digits : 3 in 100..499 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 Count : 87 Count of digits : 10 Count : 853423
Perl
<lang perl>use strict; use warnings; use feature 'say'; use Quantum::Superpositions;
sub is_strange {
my @digits = split , $_;
my @deltas = map { abs $digits[$_-1] - $digits[$_] } 1..$#digits;
all(@deltas) == any(2, 3, 5, 7);
}
my($low, $high) = (100, 500); my $cnt = my @strange = grep { is_strange($_) } $low+1 .. $high-1; say "Between $low and $high there are $cnt strange numbers:\n" .
(sprintf "@{['%5d' x $cnt]}", @strange[0..$cnt-1]) =~ s/(.{80})/$1\n/gr;</lang>
- Output:
Between 100 and 500 there are 87 strange numbers: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Phix
<lang Phix>constant diff = {-7,-5,-3,-2,2,3,5,7},
poss = apply(true,sq_add,{tagset(9,0),{diff}}),
nxts = apply(true,filter,{poss,{"in"},Template:0,9,{"[]"}})
-- nxts is {{2,3,5,7},{3,4,6,8}..., as per the factor and other entries
function strange(integer left, sequence digits, res={}, part={})
for i=1 to length(digits) do
integer di = digits[i]
if left=1 then
string fmt = join(repeat("%d",length(part)+1),"")
res = append(res,sprintf(fmt,part&di))
else
res = strange(left-1,nxts[di+1],res,part&di)
end if
end for
return res
end function
sequence res = strange(3,tagset(4)) -- (3 digit numbers beginning 1..4) printf(1,"%d strange numbers found: %s\n",{length(res),join(shorten(res,"",5),",")})</lang>
- Output:
87 strange numbers found: 130,131,135,136,138,...,479,492,494,496,497
stretch goal
Dunno when to quit, me. As there does not appear to be much interest in which 1-digits are strange, I've shown three ways to set ones (output of 0, 10, or 4). <lang Phix>constant diff = {-7,-5,-3,-2,2,3,5,7},
poss = apply(true,sq_add,{tagset(9,0),{diff}}),
nxts = apply(true,filter,{poss,{"in"},Template:0,9,{"[]"}}),
-- nxts is {{2,3,5,7},{3,4,6,8}..., as per the factor and other entries -- ones = columnize({columnize({repeat(0,10),tagset(9,0)}),repeat(0,10)}), -- ones = columnize({columnize({repeat(0,10),tagset(9,0)}),repeat(1,10)}),
ones = columnize({columnize({repeat(0,10),tagset(9,0)}),apply(tagset(9,0),is_prime)}),
twos = columnize({columnize({repeat(1,10),tagset(9,0)}),apply(nxts,length)}),
dict = new_dict(ones&twos)
function count_strange(integer left, sequence digits, atom res=0)
for i=1 to length(digits) do
integer di = digits[i]
if getd_index({left-1,di},dict)!=NULL then
res += getd({left-1,di},dict)
else
atom prev = res
res = count_strange(left-1,nxts[di+1],res)
setd({left-1,di},res-prev,dict)
end if
end for
return res
end function atom t0 = time()
atom count = count_strange(10,tagset(1)) printf(1,"There are %,d %d-digit strange numbers beginning with 1\n\n",{count,10})
for n=1 to iff(machine_bits()=32?23:28) do
printf(1,"Total %d-digit strange numbers: %,d\n",{n,count_strange(n,tagset(9,n>1))})
end for
printf(1,"(%s)\n",elapsed(time()))</lang>
- Output:
There are 853,423 10-digit strange numbers beginning with 1 Total 1-digit strange numbers: 4 Total 2-digit strange numbers: 42 Total 3-digit strange numbers: 194 Total 4-digit strange numbers: 901 Total 5-digit strange numbers: 4,178 Total 6-digit strange numbers: 19,395 Total 7-digit strange numbers: 90,011 Total 8-digit strange numbers: 417,837 Total 9-digit strange numbers: 1,939,540 Total 10-digit strange numbers: 9,003,578 Total 11-digit strange numbers: 41,795,409 Total 12-digit strange numbers: 194,020,644 Total 13-digit strange numbers: 900,672,711 Total 14-digit strange numbers: 4,181,070,893 Total 15-digit strange numbers: 19,409,220,279 Total 16-digit strange numbers: 90,100,876,862 Total 17-digit strange numbers: 418,263,512,702 Total 18-digit strange numbers: 1,941,650,412,637 Total 19-digit strange numbers: 9,013,471,997,782 Total 20-digit strange numbers: 41,842,075,002,263 Total 21-digit strange numbers: 194,238,054,320,527 Total 22-digit strange numbers: 901,686,217,399,477 Total 23-digit strange numbers: 4,185,781,417,010,380 Total 24-digit strange numbers: 19,431,112,295,670,526 Total 25-digit strange numbers: 90,202,542,361,448,337 Total 26-digit strange numbers: 418,735,609,894,371,624 Total 27-digit strange numbers: 1,943,842,229,729,877,443 Total 28-digit strange numbers: 9,023,647,681,353,485,161 (0.0s)
Python
<lang python>Strange Numbers
- isStrange :: Int -> Bool
def isStrange(n):
True if all consecutive decimal digit
pairs in n have a prime difference.
def test(a, b):
return abs(a - b) in [2, 3, 5, 7]
xs = digits(n) return all(map(test, xs, xs[1:]))
- ------------------- TEST AND DISPLAY -------------------
- main :: IO ()
def main():
List and count of Strange numbers
xs = [
n for n in range(100, 1 + 500)
if isStrange(n)
]
print('\nStrange numbers in range [100..500]\n')
print('(Total: ' + str(len(xs)) + ')\n')
print(
'\n'.join(
' '.join(
str(x) for x in row
) for row in chunksOf(10)(xs)
)
)
- ----------------------- GENERIC ------------------------
- chunksOf :: Int -> [a] -> a
def chunksOf(n):
A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divible, the final list will be shorter than n.
def go(xs):
return (
xs[i:n + i] for i in range(0, len(xs), n)
) if 0 < n else None
return go
- digits :: Int -> [Int]
def digits(n):
Component digits of a decimal number. return [int(c) for c in str(n)]
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
Strange numbers in range [100..500] (Total: 87) 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Raku
<lang perl6>sub infix:<′>(\x,\y) { abs(x - y) ∈ (2, 3, 5, 7) }
my ($low,$high) = 100, 500; my @strange.push: $_ if so all .comb.rotor(2 => -1).map: { .[0] ′ .[1] } for $low ^..^ $high;
say "Between $low and $high there are {+@strange} strange numbers:\n"; print @strange.batch(20)».fmt("%4d").join: "\n";</lang>
- Output:
Between 100 and 500 there are 87 strange numbers: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
REXX
Some optimization was added to bypass calculating the absolute value of adjacent decimal digit differences,
as well as parsing of a number to determine the differences.
<lang rexx>/*REXX pgm lists strange integers (within a range) whose decimal digs differ by a prime.*/
numeric digits 20 /*allow processing of larger numbers. */
parse arg LO HI bd . /*obtain optional arguments from the CL*/
if LO== | LO=="," then LO= 101 /*Not specified? Then use the default.*/
if HI== | HI=="," then HI= 499 /* " " " " " " */
if bd== | bd=="," then bd= /* " " " " " " */
begDig= bd\== /*look for numbers that start with:" BD*/
show= LO>0 /*indicator if the list is to be shown.*/
!.= 0; !.2= 1; !.3= 1; !.5= 1; !.7= 1 /*build array of digits that are prime.*/
LO = abs(LO) /*use the absolute value for the search*/
do p=1 for 9; _= -p; if !.p then !._= 1 /*extend array for negatives*/
end /*p*/
$= /*the list of strange numbers (so far)*/
- = 0 /* " number " " " " " */
do j=LO to HI; L= length(j) /*find for strange numbers in the range*/
if L==1 then iterate /*Number too short? Then skip it. */
if bd\== then if left(j, 1)\==bd then iterate /*Need leading dig? Maybe skip.*/
do k=1 for L-1 /*examine the difference in the digits.*/
parse var j =(k) y +1 z +1 /*get two adjacent decimal digits: Y Z */
dif= y - z /*difference between any adjacent digs.*/
if \!.dif then iterate j /*Difference not prime? Then skip it. */
end /*k*/
#= # + 1 /*bump the number of "strange" numbers.*/
if show then $= $ j /*maybe add the number to the $ list.*/
end /*j*/
/*stick a fork in it, we're all done. */
say commas(#) ' strange numbers found between ' commas(LO) " and " ,
commas(HI) ' (inclusive)'
say if show then say strip($)</lang>
- output when using the default inputs:
87 strange numbers found between 101 and 499 (inclusive) 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
- output when using the inputs of: -1000000000 2000000000 1
853,423 strange numbers found between 1,000,000,000 and 2,000,000,000 (inclusive)
Ring
<lang ring> load "stdlib.ring"
row = 0 see "Strange numbers are:" + nl
for n = 100 to 500
flag = 1
str = string(n)
for m = 1 to len(str)-1
num1 = number(str[m])
num2 = number(str[m+1])
pr = fabs(num1-num2)
if not isprime(pr)
flag = 0
exit
ok
next
if flag = 1
see str + " "
row = row + 1
if row % 10 = 0
see nl
ok
ok
next </lang>
- Output:
Strange numbers are: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Ruby
<lang ruby>def digits(n)
result = []
while n > 0
rem = n % 10
result.unshift(rem)
n = n / 10
end
return result
end
def isStrange(n)
def test(a, b)
abs = (a - b).abs
return abs == 2 || abs == 3 || abs == 5 || abs == 7
end
xs = digits(n)
for i in 1 .. xs.length - 1
if !test(xs[i - 1], xs[i]) then
return false
end
end
return true
end
xs = [] for i in 100 .. 500
if isStrange(i) then
xs << i
end
end
print "Strange numbers in range [100 .. 500]\n" print "(Total: %d)\n\n" % [xs.length]
xs.each_slice(10) do |s|
print s, "\n"
end</lang>
- Output:
Strange numbers in range [100 .. 500] (Total: 87) [130, 131, 135, 136, 138, 141, 142, 146, 147, 149] [161, 163, 164, 168, 169, 181, 183, 185, 186, 202] [203, 205, 207, 241, 242, 246, 247, 249, 250, 252] [253, 257, 258, 270, 272, 274, 275, 279, 292, 294] [296, 297, 302, 303, 305, 307, 313, 314, 316, 318] [350, 352, 353, 357, 358, 361, 363, 364, 368, 369] [381, 383, 385, 386, 413, 414, 416, 418, 420, 424] [425, 427, 429, 461, 463, 464, 468, 469, 470, 472] [474, 475, 479, 492, 494, 496, 497]
Wren
Basic task
<lang ecmascript>var primes = [2, 3, 5, 7] var count = 0 var d = [] System.print("Strange numbers in the open interval (100, 500) are:\n") for (i in 101..499) {
d.clear()
var j = i
while (j > 0) {
d.add(j % 10)
j = (j/10).floor
}
if (primes.contains((d[0] - d[1]).abs) && primes.contains((d[1] - d[2]).abs)) {
System.write("%(i) ")
count = count + 1
if (count % 10 == 0) System.print()
}
} if (count % 10 != 0) System.print() System.print("\n%(count) strange numbers in all.")</lang>
- Output:
Strange numbers in the open interval (100, 500) are: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 87 strange numbers in all.
Stretch goal
... though I've generated the 'possibles' table rather than hard-code it. Runtime about 0.085 seconds which is quick for Wren. <lang ecmascript>var diffs = [-7, -5, -3, -2, 2, 3, 5, 7] var possibles = List.filled(10, null) for (i in 0..9) {
possibles[i] = []
for (d in diffs) {
var sum = i + d
if (sum >= 0 && sum < 10) possibles[i].add(sum)
}
}
var places = 10 var start = 1 var strangeOnes = [start] for (i in 2..places) {
var newOnes = []
for (n in strangeOnes) {
for (nextN in possibles[n%10]) newOnes.add(n*10 + nextN)
}
strangeOnes = newOnes
}
System.print("Found %(strangeOnes.count) %(places)-digit strange numbers beginning with %(start).")</lang>
- Output:
Found 853423 10-digit strange numbers beginning with 1