Numbers with prime digits whose sum is 13
Find all the numbers vhich digits are primes and sum of them is 13.
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 }
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
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]