Numbers with prime digits whose sum is 13
Numbers with prime digits whose sum is 13 is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Find all the decimal numbers whose digits are all primes and sum to 13.
ALGOL W
Uses the observations about the digits and numbers in the Wren solution to generate the sequence. <lang algolw>begin
% find numbers whose digits are prime and whose digit sum is 13 %
% as noted by the Wren sample, the digits can only be 2, 3, 5, 7 %
% and there can only be 3, 4, 5 or 6 digits %
integer numberCount;
numberCount := 0;
write();
for d1 := 0, 2, 3, 5, 7 do begin
for d2 := 0, 2, 3, 5, 7 do begin
if d2 not = 0 or d1 = 0 then begin
for d3 := 0, 2, 3, 5, 7 do begin
if d3 not = 0 or ( d1 = 0 and d2 = 0 ) then begin
for d4 := 2, 3, 5, 7 do begin
for d5 := 2, 3, 5, 7 do begin
for d6 := 2, 3, 5, 7 do begin
integer sum;
sum := d1 + d2 + d3 + d4 + d5 + d6;
if sum = 13 then begin
% found a number whose prime digits sum to 13 %
integer n;
n := 0;
for d := d1, d2, d3, d4, d5, d6 do n := ( n * 10 ) + d;
writeon( i_w := 6, s_w := 1, n );
numberCount := numberCount + 1;
if numberCount rem 12 = 0 then write()
end if_sum_eq_13
end for_d6
end for_d5
end for_d4
end if_d3_ne_0_or_d1_eq_0_and_d2_e_0
end for_d3
end if_d2_ne_0_or_d1_eq_0
end for_d2
end for_d1
end.</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
AWK
<lang AWK>
- syntax: GAWK -f NUMBERS_WITH_PRIME_DIGITS_WHOSE_SUM_IS_13.AWK
BEGIN {
for (i=1; i<=1000000; i++) {
if (prime_digits_sum13(i)) {
printf("%6d ",i)
if (++count % 10 == 0) {
printf("\n")
}
}
}
printf("\n")
exit(0)
} function prime_digits_sum13(n, r,sum) {
while (n > 0) {
r = int(n % 10)
switch (r) {
case 2:
case 3:
case 5:
case 7:
break
default:
return(0)
}
n = int(n / 10)
sum += r
}
return(sum == 13)
} </lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
C
Brute force <lang c>#include <stdbool.h>
- include <stdio.h>
bool primeDigitsSum13(int n) {
int sum = 0;
while (n > 0) {
int r = n % 10;
switch (r) {
case 2:
case 3:
case 5:
case 7:
break;
default:
return false;
}
n /= 10;
sum += r;
}
return sum == 13;
}
int main() {
int i, c;
// using 2 for all digits, 6 digits is the max prior to over-shooting 13
c = 0;
for (i = 1; i < 1000000; i++) {
if (primeDigitsSum13(i)) {
printf("%6d ", i);
if (c++ == 10) {
c = 0;
printf("\n");
}
}
}
printf("\n");
return 0;
}</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
C#
Same recursive method. <lang csharp>using System; using static System.Console; using LI = System.Collections.Generic.SortedSet<int>;
class Program {
static LI unl(LI res, LI set, int lft, int mul = 1, int vlu = 0) {
if (lft == 0) res.Add(vlu);
else if (lft > 0) foreach (int itm in set)
res = unl(res, set, lft - itm, mul * 10, vlu + itm * mul);
return res; }
static void Main(string[] args) { WriteLine(string.Join(" ",
unl(new LI {}, new LI { 2, 3, 5, 7 }, 13))); }
}</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Alternate
Based in Nigel Galloway's suggestion from the discussion page. <lang csharp>class Program {
static void Main(string[] args) { int[] lst; int sum;
var w = new System.Collections.Generic.List<(int digs, int sum)> {};
foreach (int x in lst = new int[] { 2, 3, 5, 7 } ) w.Add((x, x));
while (w.Count > 0) { var i = w[0]; w.RemoveAt(0);
foreach (var j in lst) if ((sum = i.sum + j) == 13)
System.Console.Write ("{0}{1} ", i.digs, j);
else if (sum < 12)
w.Add((i.digs * 10 + j, sum)); } }
}</lang> Same output.
C++
(the alternate version)
<lang cpp>#include <cstdio>
- include <vector>
- include <bits/stdc++.h>
using namespace std;
int main() {
vector<tuple<int, int>> w; int lst[4] = { 2, 3, 5, 7 }, sum;
for (int x : lst) w.push_back({x, x});
while (w.size() > 0) { auto i = w[0]; w.erase(w.begin());
for (int x : lst) if ((sum = get<1>(i) + x) == 13)
printf("%d%d ", get<0>(i), x);
else if (sum < 12) w.push_back({get<0>(i) * 10 + x, sum}); }
return 0; }</lang>
Same output as C#.
D
<lang d>import std.stdio;
bool primeDigitsSum13(int n) {
int sum = 0;
while (n > 0) {
int r = n % 10;
switch (r) {
case 2,3,5,7:
break;
default:
return false;
}
n /= 10;
sum += r;
}
return sum == 13;
}
void main() {
// using 2 for all digits, 6 digits is the max prior to over-shooting 13
int c = 0;
for (int i = 1; i < 1_000_000; i++) {
if (primeDigitsSum13(i)) {
writef("%6d ", i);
if (c++ == 10) {
c = 0;
writeln;
}
}
}
writeln;
}</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
F#
<lang fsharp> // prime digits whose sum is 13. Nigel Galloway: October 21st., 2020 let rec fN g=let g=[for n in [2;3;5;7] do for g in g->n::g]|>List.groupBy(fun n->match List.sum n with 13->'n' |n when n<12->'g' |_->'x')|>Map.ofSeq
[yield! (if g.ContainsKey 'n' then g.['n'] else []); yield! (if g.ContainsKey 'g' then fN g.['g'] else [])]
fN [[]] |> Seq.iter(fun n->n|>List.iter(printf "%d");printf " ");printfn "" </lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Factor
Filtering selections
Generate all selections of the prime digits in the only possible lengths whose sum can be 13, then filter for sums that equal 13. <lang factor>USING: formatting io kernel math math.combinatorics math.functions math.ranges sequences sequences.extras ;
- digits>number ( seq -- n ) reverse 0 [ 10^ * + ] reduce-index ;
"Numbers whose digits are prime and sum to 13:" print { 2 3 5 7 } 3 6 [a,b] [ selections [ sum 13 = ] filter ] with map-concat [ digits>number ] map "%[%d, %]\n" printf</lang>
- Output:
Numbers whose digits are prime and sum to 13:
{ 337, 355, 373, 535, 553, 733, 2227, 2272, 2335, 2353, 2533, 2722, 3235, 3253, 3325, 3352, 3523, 3532, 5233, 5323, 5332, 7222, 22225, 22252, 22333, 22522, 23233, 23323, 23332, 25222, 32233, 32323, 32332, 33223, 33232, 33322, 52222, 222223, 222232, 222322, 223222, 232222, 322222 }
F# translation
The following is based on Nigel Galloway's algorithm as described here on the talk page. It's about 10x faster than the previous method. <lang factor>USING: io kernel math prettyprint sequences sequences.extras ;
{ } { { 2 } { 3 } { 5 } { 7 } } [
{ 2 3 5 7 } [ suffix ] cartesian-map concat
[ sum 13 = ] partition [ append ] dip [ sum 11 > ] reject
] until-empty [ bl ] [ [ pprint ] each ] interleave nl</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
FreeBASIC
Ho hum. Another prime digits task.
<lang freebasic> function digit_is_prime( n as integer ) as boolean
select case n
case 2,3,5,7
return true
case else
return false
end select
end function
function all_digits_prime( n as uinteger ) as boolean
dim as string sn = str(n)
for i as uinteger = 1 to len(sn)
if not digit_is_prime( val(mid(sn,i,1)) ) then return false
next i
return true
end function
function digit_sum_13( n as uinteger ) as boolean
dim as string sn = str(n)
dim as integer k = 0
for i as uinteger = 1 to len(sn)
k = k + val(mid(sn,i,1))
if k>13 then return false
next i
if k<>13 then return false else return true
end function
for i as uinteger = 1 to 322222
if all_digits_prime(i) andalso digit_sum_13(i) then print i,
next i</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Go
Reuses code from some other tasks. <lang go>package main
import (
"fmt" "sort" "strconv"
)
func combrep(n int, lst []byte) [][]byte {
if n == 0 {
return [][]byte{nil}
}
if len(lst) == 0 {
return nil
}
r := combrep(n, lst[1:])
for _, x := range combrep(n-1, lst) {
r = append(r, append(x, lst[0]))
}
return r
}
func shouldSwap(s []byte, start, curr int) bool {
for i := start; i < curr; i++ {
if s[i] == s[curr] {
return false
}
}
return true
}
func findPerms(s []byte, index, n int, res *[]string) {
if index >= n {
*res = append(*res, string(s))
return
}
for i := index; i < n; i++ {
check := shouldSwap(s, index, i)
if check {
s[index], s[i] = s[i], s[index]
findPerms(s, index+1, n, res)
s[index], s[i] = s[i], s[index]
}
}
}
func main() {
primes := []byte{2, 3, 5, 7}
var res []string
for n := 3; n <= 6; n++ {
reps := combrep(n, primes)
for _, rep := range reps {
sum := byte(0)
for _, r := range rep {
sum += r
}
if sum == 13 {
var perms []string
for i := 0; i < len(rep); i++ {
rep[i] += 48
}
findPerms(rep, 0, len(rep), &perms)
res = append(res, perms...)
}
}
}
res2 := make([]int, len(res))
for i, r := range res {
res2[i], _ = strconv.Atoi(r)
}
sort.Ints(res2)
fmt.Println("Those numbers whose digits are all prime and sum to 13 are:")
fmt.Println(res2)
}</lang>
- Output:
Those numbers whose digits are all prime and sum to 13 are: [337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222]
only counting
See Julia [1] <lang go> package main
import (
"fmt"
) var
Primes = []byte{2, 3, 5, 7};
var
gblCount = 0;
var
PrimesIdx = []byte{0, 1, 2, 3};
func combrep(n int, lst []byte) [][]byte {
if n == 0 {
return [][]byte{nil}
}
if len(lst) == 0 {
return nil
}
r := combrep(n, lst[1:])
for _, x := range combrep(n-1, lst) {
r = append(r, append(x, lst[0]))
}
return r
}
func Count(rep []byte)int {
var PrimCount [4]int
for i := 0; i < len(PrimCount); i++ {
PrimCount[i] = 0;
}
//get the count of every item
for i := 0; i < len(rep); i++ {
PrimCount[rep[i]]++
}
var numfac int = len(rep)
var numerator,denominator[]int
for i := 1; i <= len(rep); i++ {
numerator = append(numerator,i) // factors 1,2,3,4. n
denominator = append(denominator,1)
}
numfac = 0; //idx in denominator
for i := 0; i < len(PrimCount); i++ {
denfac := 1;
for j := 0; j < PrimCount[i]; j++ {
denominator[numfac] = denfac
denfac++
numfac++
}
}
//calculate permutations with identical items
numfac = 1;
for i := 0; i < len(numerator); i++ {
numfac = (numfac * numerator[i])/denominator[i]
}
return numfac
}
func main() {
for mySum := 2; mySum <= 103;mySum++ {
gblCount = 0;
//check for prime
for i := 2; i*i <= mySum;i++{
if mySum%i == 0 {
gblCount=1;
break
}
}
if gblCount != 0 {
continue
}
for n := 1; n <= mySum / 2 ; n++ {
reps := combrep(n, PrimesIdx)
for _, rep := range reps {
sum := byte(0)
for _, r := range rep {
sum += Primes[r]
}
if sum == byte(mySum) {
gblCount+=Count(rep);
}
}
}
fmt.Println("The count of numbers whose digits are all prime and sum to",mySum,"is",gblCount)
}
}</lang>
- Output:
The count of numbers whose digits are all prime and sum to 2 is 1 The count of numbers whose digits are all prime and sum to 3 is 1 The count of numbers whose digits are all prime and sum to 5 is 3 The count of numbers whose digits are all prime and sum to 7 is 6 The count of numbers whose digits are all prime and sum to 11 is 19 The count of numbers whose digits are all prime and sum to 13 is 43 The count of numbers whose digits are all prime and sum to 17 is 221 The count of numbers whose digits are all prime and sum to 19 is 468 The count of numbers whose digits are all prime and sum to 23 is 2098 The count of numbers whose digits are all prime and sum to 29 is 21049 The count of numbers whose digits are all prime and sum to 31 is 45148 The count of numbers whose digits are all prime and sum to 37 is 446635 The count of numbers whose digits are all prime and sum to 41 is 2061697 The count of numbers whose digits are all prime and sum to 43 is 4427752 The count of numbers whose digits are all prime and sum to 47 is 20424241 The count of numbers whose digits are all prime and sum to 53 is 202405001 The count of numbers whose digits are all prime and sum to 59 is 2005642061 The count of numbers whose digits are all prime and sum to 61 is 4307930784 The count of numbers whose digits are all prime and sum to 67 is 42688517778 The count of numbers whose digits are all prime and sum to 71 is 196942068394 The count of numbers whose digits are all prime and sum to 73 is 423011795680 The count of numbers whose digits are all prime and sum to 79 is 4191737820642 The count of numbers whose digits are all prime and sum to 83 is 19338456915087 The count of numbers whose digits are all prime and sum to 89 is 191629965405641 The count of numbers whose digits are all prime and sum to 97 is 4078672831913824 The count of numbers whose digits are all prime and sum to 101 is 18816835854129198 The count of numbers whose digits are all prime and sum to 103 is 40416663565084464 real 0m4,489s user 0m5,584s sys 0m0,188s
Haskell
As an unfold, in the recursive pattern described by Nigel Galloway on the Talk page. <lang haskell>import Data.List.Split (chunksOf) import Data.List (intercalate, transpose, unfoldr) import Text.Printf
primeDigitsNumsSummingToN :: Int -> [Int] primeDigitsNumsSummingToN n = concat $ unfoldr go (return <$> primeDigits)
where primeDigits = [2, 3, 5, 7] go :: Int -> Maybe ([Int], Int) go xs | null xs = Nothing | otherwise = Just (nextLength xs) nextLength :: Int -> ([Int], Int) nextLength xs = let harvest nv = [ unDigits $ fst nv | n == snd nv ] prune nv = [ fst nv | pred n > snd nv ] in ((,) . concatMap harvest <*> concatMap prune) (((,) <*> sum) <$> ((<$> xs) . (<>) . return =<< primeDigits))
TEST -------------------------
main :: IO () main = do
let n = 13
xs = primeDigitsNumsSummingToN n
mapM_
putStrLn
[ concat
[ (show . length) xs
, " numbers with prime digits summing to "
, show n
, ":\n"
]
, table " " $ chunksOf 10 (show <$> xs)
]
table :: String -> String -> String table gap rows =
let ic = intercalate
ws = maximum . fmap length <$> transpose rows
pw = printf . flip ic ["%", "s"] . show
in unlines $ ic gap . zipWith pw ws <$> rows
unDigits :: [Int] -> Int unDigits = foldl ((+) . (10 *)) 0</lang>
- Output:
43 numbers with prime digits summing to 13: 337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Java
<lang java>public class PrimeDigits {
private static boolean primeDigitsSum13(int n) {
int sum = 0;
while (n > 0) {
int r = n % 10;
if (r != 2 && r != 3 && r != 5 && r != 7) {
return false;
}
n /= 10;
sum += r;
}
return sum == 13;
}
public static void main(String[] args) {
// using 2 for all digits, 6 digits is the max prior to over-shooting 13
int c = 0;
for (int i = 1; i < 1_000_000; i++) {
if (primeDigitsSum13(i)) {
System.out.printf("%6d ", i);
if (c++ == 10) {
c = 0;
System.out.println();
}
}
}
System.out.println();
}
}</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
JavaScript
As an unfold, in the recursive pattern described by Nigel Galloway on the Talk page. <lang javascript>(() => {
'use strict';
// ---- NUMBERS WITH PRIME DIGITS WHOSE SUM IS 13 ----
// primeDigitsSummingToN :: Int -> [Int]
const primeDigitsSummingToN = n => {
const primeDigits = [2, 3, 5, 7];
const go = xs =>
fanArrow(
concatMap( // Harvested,
nv => n === nv[1] ? (
[unDigits(nv[0])]
) : []
)
)(
concatMap( // Pruned.
nv => pred(n) > nv[1] ? (
[nv[0]]
) : []
)
)(
// Existing numbers with prime digits appended,
// tupled with the resulting digit sums.
xs.flatMap(
ds => primeDigits.flatMap(d => [
fanArrow(identity)(sum)(
ds.concat(d)
)
])
)
);
return concat(
unfoldr(
xs => 0 < xs.length ? (
Just(go(xs))
) : Nothing()
)(
primeDigits.map(pureList)
)
);
}
// ---------------------- TEST -----------------------
// main :: IO ()
const main = () =>
chunksOf(6)(
primeDigitsSummingToN(13)
).forEach(
x => console.log(x)
)
// ---------------- GENERIC FUNCTIONS ----------------
// Just :: a -> Maybe a
const Just = x => ({
type: 'Maybe',
Nothing: false,
Just: x
});
// Nothing :: Maybe a
const Nothing = () => ({
type: 'Maybe',
Nothing: true,
});
// Tuple (,) :: a -> b -> (a, b)
const Tuple = a =>
b => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});
// chunksOf :: Int -> [a] -> a const chunksOf = n => xs => enumFromThenTo(0)(n)( xs.length - 1 ).reduce( (a, i) => a.concat([xs.slice(i, (n + i))]), [] );
// concat :: a -> [a] // concat :: [String] -> String const concat = xs => ( ys => 0 < ys.length ? ( ys.every(Array.isArray) ? ( [] ) : ).concat(...ys) : ys )(list(xs));
// concatMap :: (a -> [b]) -> [a] -> [b]
const concatMap = f =>
xs => xs.flatMap(f)
// enumFromThenTo :: Int -> Int -> Int -> [Int]
const enumFromThenTo = x1 =>
x2 => y => {
const d = x2 - x1;
return Array.from({
length: Math.floor(y - x2) / d + 2
}, (_, i) => x1 + (d * i));
};
// fanArrow (&&&) :: (a -> b) -> (a -> c) -> (a -> (b, c))
const fanArrow = f =>
// A function from x to a tuple of (f(x), g(x))
// ((,) . f <*> g)
g => x => Tuple(f(x))(
g(x)
);
// identity :: a -> a
const identity = x =>
// The identity function.
x;
// list :: StringOrArrayLike b => b -> [a]
const list = xs =>
// xs itself, if it is an Array,
// or an Array derived from xs.
Array.isArray(xs) ? (
xs
) : Array.from(xs || []);
// pred :: Enum a => a -> a
const pred = x =>
x - 1;
// pureList :: a -> [a] const pureList = x => [x];
// sum :: [Num] -> Num
const sum = xs =>
// The numeric sum of all values in xs.
xs.reduce((a, x) => a + x, 0);
// unDigits :: [Int] -> Int
const unDigits = ds =>
// The integer with the given digits.
ds.reduce((a, x) => 10 * a + x, 0);
// The 'unfoldr' function is a *dual* to 'foldr': // while 'foldr' reduces a list to a summary value, // 'unfoldr' builds a list from a seed value.
// unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
const unfoldr = f =>
v => {
const xs = [];
let xr = [v, v];
while (true) {
const mb = f(xr[1]);
if (mb.Nothing) {
return xs;
} else {
xr = mb.Just;
xs.push(xr[0]);
}
}
};
return main();
})();</lang>
- Output:
337,355,373,535,553,733 2227,2272,2335,2353,2533,2722 3235,3253,3325,3352,3523,3532 5233,5323,5332,7222,22225,22252 22333,22522,23233,23323,23332,25222 32233,32323,32332,33223,33232,33322 52222,222223,222232,222322,223222,232222 322222
Julia
<lang julia>using Combinatorics, Primes
function primedigitsums(targetsum)
possibles = mapreduce(x -> fill(x, div(targetsum, x)), vcat, [2, 3, 5, 7])
a = map(x -> evalpoly(BigInt(10), x),
mapreduce(x -> unique(collect(permutations(x))), vcat,
unique(filter(x -> sum(x) == targetsum, collect(combinations(possibles))))))
println("There are $(length(a)) prime-digit-only numbers summing to $targetsum : $a")
end
foreach(primedigitsums, [5, 7, 11, 13])
function primedigitcombos(targetsum)
possibles = [2, 3, 5, 7]
found = Vector{Vector{Int}}()
combos = [Int[]]
tempcombos = Vector{Vector{Int}}()
newcombos = Vector{Vector{Int}}()
while !isempty(combos)
for combo in combos, j in possibles
csum = sum(combo) + j
if csum <= targetsum
newcombo = sort!([combo; j])
csum < targetsum && !(newcombo in newcombos) && push!(newcombos, newcombo)
csum == targetsum && !(newcombo in found) && push!(found, newcombo)
end
end
empty!(combos)
tempcombos = combos
combos = newcombos
newcombos = tempcombos
end
return found
end
function countprimedigitsums(targetsum)
found = primedigitcombos(targetsum)
total = sum(arr -> factorial(BigInt(length(arr))) ÷
prod(x -> factorial(BigInt(count(y -> y == x, arr))), unique(arr)), found)
println("There are $total prime-digit-only numbers summing to $targetsum.")
end
foreach(countprimedigitsums, nextprimes(17, 40))
</lang>
- Output:
There are 3 prime-digit-only numbers summing to 5 : [5, 32, 23] There are 6 prime-digit-only numbers summing to 7 : [7, 52, 25, 322, 232, 223] There are 19 prime-digit-only numbers summing to 11 : [722, 272, 227, 533, 353, 335, 5222, 2522, 2252, 2225, 3332, 3323, 3233, 2333, 32222, 23222, 22322, 22232, 22223] There are 43 prime-digit-only numbers summing to 13 : [733, 373, 337, 553, 535, 355, 7222, 2722, 2272, 2227, 5332, 3532, 3352, 5323, 3523, 5233, 2533, 3253, 2353, 3325, 3235, 2335, 52222, 25222, 22522, 22252, 22225, 33322, 33232, 32332, 23332, 33223, 32323, 23323, 32233, 23233, 22333, 322222, 232222, 223222, 222322, 222232, 222223] There are 221 prime-digit-only numbers summing to 17. There are 468 prime-digit-only numbers summing to 19. There are 2098 prime-digit-only numbers summing to 23. There are 21049 prime-digit-only numbers summing to 29. There are 45148 prime-digit-only numbers summing to 31. There are 446635 prime-digit-only numbers summing to 37. There are 2061697 prime-digit-only numbers summing to 41. There are 4427752 prime-digit-only numbers summing to 43. There are 20424241 prime-digit-only numbers summing to 47. There are 202405001 prime-digit-only numbers summing to 53. There are 2005642061 prime-digit-only numbers summing to 59. There are 4307930784 prime-digit-only numbers summing to 61. There are 42688517778 prime-digit-only numbers summing to 67. There are 196942068394 prime-digit-only numbers summing to 71. There are 423011795680 prime-digit-only numbers summing to 73. There are 4191737820642 prime-digit-only numbers summing to 79. There are 19338456915087 prime-digit-only numbers summing to 83. There are 191629965405641 prime-digit-only numbers summing to 89. There are 4078672831913824 prime-digit-only numbers summing to 97. There are 18816835854129198 prime-digit-only numbers summing to 101. There are 40416663565084464 prime-digit-only numbers summing to 103. There are 186461075642340151 prime-digit-only numbers summing to 107. There are 400499564627237889 prime-digit-only numbers summing to 109. There are 1847692833654336940 prime-digit-only numbers summing to 113. There are 389696778451488128521 prime-digit-only numbers summing to 127. There are 1797854500757846669066 prime-digit-only numbers summing to 131. There are 17815422682488317051838 prime-digit-only numbers summing to 137. There are 38265729200380568226735 prime-digit-only numbers summing to 139. There are 1749360471151229472803187 prime-digit-only numbers summing to 149. There are 3757449669085729778349997 prime-digit-only numbers summing to 151. There are 37233577041224219717325533 prime-digit-only numbers summing to 157. There are 368957506121989278337474430 prime-digit-only numbers summing to 163. There are 1702174484494837917764813972 prime-digit-only numbers summing to 167. There are 16867303726643249517987636148 prime-digit-only numbers summing to 173. There are 167142638782573042636172836062 prime-digit-only numbers summing to 179. There are 359005512666242240589945886415 prime-digit-only numbers summing to 181. There are 16412337250779890525195727788488 prime-digit-only numbers summing to 191. There are 35252043354611887665339338710961 prime-digit-only numbers summing to 193. There are 162634253887997896351270835136345 prime-digit-only numbers summing to 197. There are 349321957098598244959032342621956 prime-digit-only numbers summing to 199.
Kotlin
<lang scala>fun primeDigitsSum13(n: Int): Boolean {
var nn = n
var sum = 0
while (nn > 0) {
val r = nn % 10
if (r != 2 && r != 3 && r != 5 && r != 7) {
return false
}
nn /= 10
sum += r
}
return sum == 13
}
fun main() {
// using 2 for all digits, 6 digits is the max prior to over-shooting 13
var c = 0
for (i in 1 until 1000000) {
if (primeDigitsSum13(i)) {
print("%6d ".format(i))
if (c++ == 10) {
c = 0
println()
}
}
}
println()
}</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Nim
<lang Nim>import math, sequtils, strutils
type Digit = 0..9
proc toInt(s: seq[Digit]): int =
## Convert a sequence of digits to an integer. for n in s: result = 10 * result + n
const PrimeDigits = @[Digit 2, 3, 5, 7]
var list = PrimeDigits.mapIt(@[it]) # List of sequences of digits. var result: seq[int] while list.len != 0:
var nextList: seq[seq[Digit]] # List with one more digit.
for digitSeq in list:
let currSum = sum(digitSeq)
for n in PrimeDigits:
let newSum = currSum + n
let newDigitSeq = digitSeq & n
if newSum < 13: nextList.add newDigitSeq
elif newSum == 13: result.add newDigitSeq.toInt
else: break
list = move(nextList)
for i, n in result:
stdout.write ($n).align(6), if (i + 1) mod 9 == 0: '\n' else: ' '
echo()</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Pascal
Only counting.
Extreme fast in finding the sum of primesdigits = value.
Limited by Uint64
<lang pascal>program PrimSumUpTo13; {$IFDEF FPC}
{$MODE DELPHI}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF} uses
sysutils;
type
tDigits = array[0..3] of Uint32;
const
MAXNUM = 113;
var
gblPrimDgtCnt :tDigits; gblCount: NativeUint;
function isPrime(n: NativeUint):boolean; var
i : NativeUInt;
Begin
result := (n>1);
if n<4 then
EXIT;
result := false;
if n AND 1 = 0 then
EXIT;
i := 3;
while i*i<= n do
Begin
If n MOD i = 0 then
EXIT;
inc(i,2);
end;
result := true;
end;
procedure Sort(var t:tDigits); var
i,j,k: NativeUint; temp : Uint32;
Begin
For k := 0 to high(tdigits)-1 do
Begin
temp:= t[k];
j := k;
For i := k+1 to high(tdigits) do
Begin
if temp < t[i] then
Begin
temp := t[i];
j := i;
end;
end;
t[j] := t[k];
t[k] := temp;
end;
end;
function CalcPermCount:NativeUint; //TempDgtCnt[0] = 3 and TempDgtCnt[1..3]= 2 -> dgtcnt = 3+3*2= 9 //permcount = dgtcnt! /(TempDgtCnt[0]!*TempDgtCnt[1]!*TempDgtCnt[2]!*TempDgtCnt[3]!); //nom of n! = 1,2,3, 4,5, 6,7, 8,9 //denom = 1,2,3, 1,2, 1,2, 1,2 var
TempDgtCnt : tdigits; i,f : NativeUint;
begin
TempDgtCnt := gblPrimDgtCnt; Sort(TempDgtCnt); //jump over 1/1*2/2*3/3*4/4*..* TempDgtCnt[0]/TempDgtCnt[0] f := TempDgtCnt[0]+1; result :=1;
For i := 1 to TempDgtCnt[1] do Begin result := (result*f) DIV i; inc(f); end; For i := 1 to TempDgtCnt[2] do Begin result := (result*f) DIV i; inc(f); end; For i := 1 to TempDgtCnt[3] do Begin result := (result*f) DIV i; inc(f); end;
end;
procedure check32(sum3 :NativeUint); var
n3 : nativeInt;
begin
n3 := sum3 DIV 3;
gblPrimDgtCnt[1]:= 0;
while n3 >= 0 do
begin
//divisible by 2
if sum3 AND 1 = 0 then
Begin
gblPrimDgtCnt[0] := sum3 shr 1;
inc(gblCount,CalcPermCount);
sum3 -= 3;
inc(gblPrimDgtCnt[1]);
dec(n3);
end;
sum3 -= 3;
inc(gblPrimDgtCnt[1]);
dec(n3);
end;
end;
var
Num : NativeUint; i,sum7,sum5: NativeInt;
BEGIN
writeln('Sum':6,'Count of arrangements':25);
Num := 1;
repeat
inc(num);
if Not(isPrime(Num)) then
CONTINUE;
gblCount := 0;
sum7 :=num;
gblPrimDgtCnt[3] := 0;
while sum7 >=0 do
Begin
sum5 := sum7;
gblPrimDgtCnt[2]:=0;
while sum5 >= 0 do
Begin
check32(sum5);
dec(sum5,5);
inc(gblPrimDgtCnt[2]);
end;
inc(gblPrimDgtCnt[3]);
dec(sum7,7);
end;
writeln(num:6,gblCount:25,' ');
until num > MAXNUM;
END.</lang>
- Output:
Sum Count of arrangements
2 1
3 1
5 3
7 6
11 19
13 43
17 221
19 468
23 2098
29 21049
31 45148
37 446635
41 2061697
43 4427752
47 20424241
53 202405001
59 2005642061
61 4307930784
67 42688517778
71 196942068394
73 423011795680
79 4191737820642
83 19338456915087
89 191629965405641
97 4078672831913824
101 18816835854129198
103 40416663565084464
107 186461075642340151
109 400499564627237889
113 1847692833654336940
real 0m0,003s
using gmp
<lang pascal>program PrimSumUpTo13_GMP; {$IFDEF FPC}
{$OPTIMIZATION ON,ALL}
{$MODE DELPHI}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF} uses
sysutils,gmp;
type
tDigits = array[0..3] of Uint32;
const
MAXNUM = 199;//999
var
//split factors of n! in Uint64 groups Fakul : array[0..MAXNUM] of UInt64; IdxLimits : array[0..MAXNUM DIV 3] of word; gblPrimDgtCnt :tDigits;
gblSum, gbldelta : MPInteger; // multi precision (big) integers selve cleaning s : AnsiString;
procedure Init; var
i,j,tmp,n :NativeUint;
Begin
//generate n! by Uint64 factors
j := 1;
n := 0;
For i := 1 to MAXNUM do
begin
tmp := j;
j *= i;
if j div i <> tmp then
Begin
IdxLimits[n]:= i-1;
j := i;
inc(n);
end;
Fakul[i] := j;
end;
setlength(s,512);// 997 -> 166 z_init_set_ui(gblSum,0); z_init_set_ui(gbldelta,0);
end;
function isPrime(n: NativeUint):boolean; var
i : NativeUInt;
Begin
result := (n>1);
if n<4 then
EXIT;
result := false;
if n AND 1 = 0 then
EXIT;
i := 3;
while i*i<= n do
Begin
If n MOD i = 0 then
EXIT;
inc(i,2);
end;
result := true;
end;
procedure Sort(var t:tDigits); // sorting descending to reduce calculations var
i,j,k: NativeUint; temp : Uint32;
Begin
For k := 0 to high(tdigits)-1 do
Begin
temp:= t[k];
j := k;
For i := k+1 to high(tdigits) do
Begin
if temp < t[i] then
Begin
temp := t[i];
j := i;
end;
end;
t[j] := t[k];
t[k] := temp;
end;
end;
function calcOne(f,n: NativeUint):NativeUint; var
i,idx,MaxMulLmt : NativeUint;
Begin
result := f; if n = 0 then EXIT;
MaxMulLmt := High(MaxMulLmt) DIV (f+n);
z_mul_ui(gbldelta,gbldelta,result);
inc(result);
if n > 1 then
Begin
//multiply by parts of (f+n)!/f! with max Uint64 factors
i := 2;
while (i<=n) do
begin
idx := 1;
while (i<=n) AND (idx<MaxMulLmt) do
Begin
idx *= result;
inc(i);
inc(result);
end;
z_mul_ui(gbldelta,gbldelta,idx);
end;
//divide by n! with max Uint64 divisors
idx := 0;
if n > IdxLimits[idx] then
repeat
z_divexact_ui(gbldelta,gbldelta,Fakul[IdxLimits[idx]]);
inc(idx);
until IdxLimits[idx] >= n;
z_divexact_ui(gbldelta,gbldelta,Fakul[n]);
end;
end;
procedure CalcPermCount; //TempDgtCnt[0] = 3 and TempDgtCnt[1..3]= 2 -> dgtcnt = 3+3*2= 9 //permcount = dgtcnt! /(TempDgtCnt[0]!*TempDgtCnt[1]!*TempDgtCnt[2]!*TempDgtCnt[3]!); //nom of n! = 1,2,3, 4,5, 6,7, 8,9 //denom = 1,2,3, 1,2, 1,2, 1,2 var
TempDgtCnt : tdigits; f : NativeUint;
begin
TempDgtCnt := gblPrimDgtCnt; Sort(TempDgtCnt); //jump over 1/1*2/2*3/3*4/4*..* //res := 1; f := TempDgtCnt[0]+1; z_set_ui(gbldelta,1);
f := calcOne(f,TempDgtCnt[1]); f := calcOne(f,TempDgtCnt[2]); f := calcOne(f,TempDgtCnt[3]);
z_add(gblSum,gblSum,gblDelta);
end;
procedure check32(sum3 :NativeInt); var
n3 : nativeInt;
begin
n3 := sum3 DIV 3;
gblPrimDgtCnt[1]:= 0;
while n3 >= 0 do
begin
//divisible by 2
if sum3 AND 1 = 0 then
Begin
gblPrimDgtCnt[0] := sum3 shr 1;
CalcPermCount;
end;
sum3 -= 3;
inc(gblPrimDgtCnt[1]);
dec(n3);
end;
end; procedure CheckAll(num:NativeUint); var
sum7,sum5: NativeInt;
BEGIN
z_set_ui(gblSum,0);
sum7 :=num;
gblPrimDgtCnt[3] := 0;
while sum7 >=0 do
Begin
sum5 := sum7;
gblPrimDgtCnt[2]:=0;
while sum5 >= 0 do
Begin
check32(sum5);
dec(sum5,5);
inc(gblPrimDgtCnt[2]);
end;
inc(gblPrimDgtCnt[3]);
dec(sum7,7);
end;
end;
var
T0 : Int64; Num : NativeUint;
BEGIN
Init;
T0 := GettickCount64;
// Number crunching goes here
writeln('Sum':6,'Count of arrangements':25);
For num := 2 to MAXNUM do
IF isPrime(Num) then
Begin
CheckAll(num);
z_get_str(pChar(s),10,gblSum);
writeln(num:6,' ',pChar(s));
end;
writeln('Time taken : ',GettickCount64-T0,' ms');
z_clear(gblSum); z_clear(gbldelta);
END.</lang>
- Output:
tio.run/#pascal-fpc
Sum Count of arrangements
2 1
3 1
5 3
7 6
11 19
13 43
17 221
19 468
23 2098
29 21049
31 45148
37 446635
41 2061697
43 4427752
47 20424241
53 202405001
59 2005642061
61 4307930784
67 42688517778
71 196942068394
73 423011795680
79 4191737820642
83 19338456915087
89 191629965405641
97 4078672831913824
101 18816835854129198
103 40416663565084464
107 186461075642340151
109 400499564627237889
113 1847692833654336940
127 389696778451488128521
131 1797854500757846669066
137 17815422682488317051838
139 38265729200380568226735
149 1749360471151229472803187
151 3757449669085729778349997
157 37233577041224219717325533
163 368957506121989278337474430
167 1702174484494837917764813972
173 16867303726643249517987636148
179 167142638782573042636172836062
181 359005512666242240589945886415
191 16412337250779890525195727788488
193 35252043354611887665339338710961
197 162634253887997896351270835136345
199 349321957098598244959032342621956
Time taken : 23 ms
Perl
<lang perl>#!/usr/bin/perl
use strict; use warnings;
my @queue = my @primedigits = ( 2, 3, 5, 7 ); my $numbers;
while( my $n = shift @queue )
{
if( eval $n == 13 )
{
$numbers .= $n =~ tr/+//dr . " ";
}
elsif( eval $n < 13 )
{
push @queue, map "$n+$_", @primedigits;
}
}
print $numbers =~ s/.{1,80}\K /\n/gr;</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Phix
with javascript_semantics function unlucky(sequence set, integer needed, string v="", sequence res={}) if needed=0 then res = append(res,sprintf("%6s",v)) elsif needed>0 then for i=length(set) to 1 by -1 do res = unlucky(set,needed-set[i],(set[i]+'0')&v,res) end for end if return res end function sequence r = sort(unlucky({2,3,5,7},13)) puts(1,join_by(r,1,11," "))
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
iterative
Queue-based version of Nigel's recursive algorithm, same output.
with javascript_semantics requires("0.8.2") -- uses latest apply() mods, rest is fine constant dgts = {2,3,5,7} function unlucky() sequence res = {}, q = {{0,0}} integer s, -- partial digit sum, <=11 v -- corresponding value while length(q) do {{s,v}, q} = {q[1], q[2..$]} for i=1 to length(dgts) do integer d = dgts[i], {ns,nv} = {s+d,v*10+d} if ns<=11 then q &= {{ns,nv}} elsif ns=13 then res &= nv end if end for end while return res end function sequence r = unlucky() r = apply(true,sprintf,{{"%6d"},r}) puts(1,join_by(r,1,11," "))
I've archived a slightly more OTT version: Numbers_with_prime_digits_whose_sum_is_13/Phix.
Prolog
<lang Prolog> digit_sum(N, M) :- digit_sum(N, 0, M). digit_sum(0, A, B) :- !, A = B. digit_sum(N, A0, M) :-
divmod(N, 10, Q, R), plus(A0, R, A1), digit_sum(Q, A1, M).
prime_digits(0). prime_digits(N) :-
prime_digits(M), member(D, [2, 3, 5, 7]), N is 10 * M + D.
prime13(N) :-
prime_digits(N), (N > 333_333 -> !, false ; true), digit_sum(N, 13).
main :-
findall(N, prime13(N), S),
format("Those numbers whose digits are all prime and sum to 13 are: ~n~w~n", [S]),
halt.
?- main. </lang>
- Output:
Those numbers whose digits are all prime and sum to 13 are: [337,355,373,535,553,733,2227,2272,2335,2353,2533,2722,3235,3253,3325,3352,3523,3532,5233,5323,5332,7222,22225,22252,22333,22522,23233,23323,23332,25222,32233,32323,32332,33223,33232,33322,52222,222223,222232,222322,223222,232222,322222]
Raku
<lang perl6>put join ', ', sort +*, unique flat
< 2 2 2 2 2 3 3 3 5 5 7 >.combinations
.grep( *.sum == 13 )
.map( { .join => $_ } )
.map: { .value.permutations».join }</lang>
- Output:
337, 355, 373, 535, 553, 733, 2227, 2272, 2335, 2353, 2533, 2722, 3235, 3253, 3325, 3352, 3523, 3532, 5233, 5323, 5332, 7222, 22225, 22252, 22333, 22522, 23233, 23323, 23332, 25222, 32233, 32323, 32332, 33223, 33232, 33322, 52222, 222223, 222232, 222322, 223222, 232222, 322222
REXX
<lang rexx>/*REXX pgm finds and displays all decimal numbers whose digits are prime and sum to 13. */ LO= 337; HI= 322222; #= 0 /*define low&high range for #s; # count*/ $= /*variable to hold the list of #s found*/
do j=LO for HI-LO+1 /*search for numbers in this range. */
if verify(j, 2357) \== 0 then iterate /*J must be comprised of prime digits.*/
parse var j a 2 b 3 -1 z /*parse: 1st, 2nd, & last decimal digs.*/
sum= a + b + z /*sum: " " " " " " */
do k=3 for length(j)-3 /*only need to sum #s with #digits ≥ 4 */
sum= sum + substr(j, k, 1) /*sum some middle decimal digits of J.*/
end /*k*/
if sum\==13 then iterate /*Sum not equal to 13? Then skip this #*/
#= # + 1; $= $ j /*bump # count; append # to the $ list.*/
end /*j*/
say strip($); say /*display the output list to the term. */ say # ' decimal numbers found whose digits are prime and the decimal digits sum to 13'</lang>
- output when using the internal default inputs:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222 43 decimal numbers found whose digits are prime and the decimal digits sum to 13
Ring
<lang ring> load "stdlib.ring"
sum = 0 limit = 1000000 aPrimes = []
for n = 1 to limit
sum = 0
st = string(n)
for m = 1 to len(st)
num = number(st[m])
if isprime(num)
sum = sum + num
flag = 1
else
flag = 0
exit
ok
next
if flag = 1 and sum = 13
add(aPrimes,n)
ok
next
see "Unlucky numbers are:" + nl see showArray(aPrimes)
func showarray vect
svect = ""
for n in vect
svect += "" + n + ","
next
? "[" + left(svect, len(svect) - 1) + "]"
</lang>
- Output:
Unlucky numbers are: [337,355,373,535,553,733,2227,2272,2335,2353,2533,2722,3235,3253,3325,3352,3523,3532,5233,5323,5332,7222,22225,22252,22333,22522,23233,23323,23332,25222,32233,32323,32332,33223,33232,33322,52222,222223,222232,222322,223222,232222,322222]
Ruby
<lang ruby>def primeDigitsSum13(n)
sum = 0
while n > 0
r = n % 10
if r != 2 and r != 3 and r != 5 and r != 7 then
return false
end
n = (n / 10).floor
sum = sum + r
end
return sum == 13
end
c = 0 for i in 1 .. 1000000
if primeDigitsSum13(i) then
print "%6d " % [i]
if c == 10 then
c = 0
print "\n"
else
c = c + 1
end
end
end print "\n" </lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Visual Basic .NET
Same recursive method. <lang vbnet>Imports System Imports System.Console Imports LI = System.Collections.Generic.SortedSet(Of Integer)
Module Module1
Function unl(ByVal res As LI, ByVal lst As LI, ByVal lft As Integer, ByVal Optional mul As Integer = 1, ByVal Optional vlu As Integer = 0) As LI
If lft = 0 Then
res.Add(vlu)
ElseIf lft > 0 Then
For Each itm As Integer In lst
res = unl(res, lst, lft - itm, mul * 10, vlu + itm * mul)
Next
End If
Return res
End Function
Sub Main(ByVal args As String())
WriteLine(string.Join(" ",
unl(new LI From {}, new LI From { 2, 3, 5, 7 }, 13)))
End Sub
End Module</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222
Alternate
Thanks to Nigel Galloway's suggestion from the discussion page. <lang vbnet>Imports Tu = System.Tuple(Of Integer, Integer)
Module Module1
Sub Main()
Dim w As New List(Of Tu), sum, x As Integer,
lst() As Integer = { 2, 3, 5, 7 }
For Each x In lst : w.Add(New Tu(x, x)) : Next
While w.Count > 0 : With w(0) : For Each j As Integer In lst
sum = .Item2 + j
If sum = 13 Then Console.Write("{0}{1} ", .Item1, j)
If sum < 12 Then w.Add(New Tu(.Item1 * 10 + j, sum))
Next : End With : w.RemoveAt(0) : End While
End Sub
End Module</lang> Same output.
Wren
As the only digits which are prime are [2, 3, 5, 7], it is clear that a number must have between 3 and 6 digits for them to sum to 13. <lang ecmascript>import "/math" for Nums import "/seq" for Lst import "/sort" for Sort
var combrep // recursive combrep = Fn.new { |n, lst|
if (n == 0 ) return [[]]
if (lst.count == 0) return []
var r = combrep.call(n, lst[1..-1])
for (x in combrep.call(n-1, lst)) {
var y = x.toList
y.add(lst[0])
r.add(y)
}
return r
}
var permute // recursive permute = Fn.new { |input|
if (input.count == 1) return [input]
var perms = []
var toInsert = input[0]
for (perm in permute.call(input[1..-1])) {
for (i in 0..perm.count) {
var newPerm = perm.toList
newPerm.insert(i, toInsert)
perms.add(newPerm)
}
}
return perms
}
var primes = [2, 3, 5, 7] var res = [] for (n in 3..6) {
var reps = combrep.call(n, primes)
for (rep in reps) {
if (Nums.sum(rep) == 13) {
var perms = permute.call(rep)
for (i in 0...perms.count) perms[i] = Num.fromString(perms[i].join())
res.addAll(Lst.distinct(perms))
}
}
} Sort.quick(res) System.print("Those numbers whose digits are all prime and sum to 13 are:") System.print(res)</lang>
- Output:
Those numbers whose digits are all prime and sum to 13 are: [337, 355, 373, 535, 553, 733, 2227, 2272, 2335, 2353, 2533, 2722, 3235, 3253, 3325, 3352, 3523, 3532, 5233, 5323, 5332, 7222, 22225, 22252, 22333, 22522, 23233, 23323, 23332, 25222, 32233, 32323, 32332, 33223, 33232, 33322, 52222, 222223, 222232, 222322, 223222, 232222, 322222]
XPL0
<lang XPL0> int N, M, S, D; [for N:= 2 to 322222 do
[M:= N; S:= 0;
repeat M:= M/10; \get digit D
D:= remainder(0);
case D of
2, 3, 5, 7:
[S:= S+D;
if S=13 and M=0 \all digits included\ then
[IntOut(0, N); ChOut(0, ^ )];
]
other M:= 0; \digit not prime so exit repeat loop
until M=0; \all digits in N tested or digit not prime
];
]</lang>
- Output:
337 355 373 535 553 733 2227 2272 2335 2353 2533 2722 3235 3253 3325 3352 3523 3532 5233 5323 5332 7222 22225 22252 22333 22522 23233 23323 23332 25222 32233 32323 32332 33223 33232 33322 52222 222223 222232 222322 223222 232222 322222