Numbers with prime digits whose sum is 13
Find all the 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
Factor
<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 }
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]
Julia
<lang julia>using Combinatorics
function primedigitsums(targetsum)
possibles = mapreduce(x -> fill(x, div(targetsum, x)), vcat, [2, 3, 5, 7])
a = map(x -> evalpoly(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])
</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]
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 /*define the low and high range for #s.*/ pDigs= 2357; #= 0 /*define prime digits; found #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, pDigs) \== 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]
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 [] System.write("") // guard against VM recursion bug 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] System.write("") // guard against VM recursion bug 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]