Composite numbers k with no single digit factors whose factors are all substrings of k

Find the composite numbers k in base 10, that have no single digit prime factors and whose prime factors are all a substring of k.

Task

Find and show here, on this page, the first ten elements of the sequence.

Stretch

Find and show the next ten elements.

Julia

<lang julia>using Lazy using Primes

function containsitsonlytwodigfactors(n)

   s = string(n)
   return !isprime(n) && all(t -> length(t) > 1 && contains(s, t), map(x -> string(x), collect(keys(factor(n)))))

end

seq = @>> Lazy.range(2) filter(containsitsonlytwodigfactors)

foreach(p -> print(lpad(last(p), 9), first(p) == 10 ? "\n" : ""), enumerate(take(20, seq)))

</lang>

Output:

    15317    59177    83731   119911   183347   192413  1819231  2111317  2237411  3129361
  5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827

Phix

Translation of: Wren

with javascript_semantics
integer count = 0, n = 11*11,
        limit = iff(platform()=JS?10:20)
atom t0 = time(), t1 = time()
while count<limit do
    if gcd(n,3*5*7)=1 then
        sequence f = prime_factors(n,true,-1)
        if length(f)>1 then
            string s = sprintf("%d",n)
            bool valid = true
            for i=1 to length(f) do
                if (i=1 or f[i]!=f[i-1])
                and not match(sprintf("%d",f[i]),s) then
                    valid = false
                    exit
                end if
            end for
            if valid then
                count += 1
                string t = join(apply(f,sprint),"x"),
                       e = elapsed(time()-t1)
                printf(1,"%2d: %,10d = %-17s (%s)\n",{count,n,t,e})
                t1 = time()
            end if
        end if
    end if
    n += 2
end while
printf(1,"Total time:%s\n",{elapsed(time()-t0)})

Output:

(As usual, limiting to the first 10 under pwa/p2js keeps the time staring at a blank screen under 10s)

 1:     15,317 = 17x17x53          (0s)
 2:     59,177 = 17x59x59          (0.1s)
 3:     83,731 = 31x37x73          (0.0s)
 4:    119,911 = 11x11x991         (0.0s)
 5:    183,347 = 47x47x83          (0.1s)
 6:    192,413 = 13x19x19x41       (0.0s)
 7:  1,819,231 = 19x23x23x181      (3.5s)
 8:  2,111,317 = 13x13x13x31x31    (0.7s)
 9:  2,237,411 = 11x11x11x41x41    (0.4s)
10:  3,129,361 = 29x29x61x61       (2.6s)
11:  5,526,173 = 17x61x73x73       (7.5s)
12: 11,610,313 = 11x11x11x11x13x61 (23.2s)
13: 13,436,683 = 13x13x43x43x43    (7.9s)
14: 13,731,373 = 73x137x1373       (1.3s)
15: 13,737,841 = 13x13x13x13x13x37 (0.0s)
16: 13,831,103 = 11x13x311x311     (0.4s)
17: 15,813,251 = 251x251x251       (8.9s)
18: 17,692,313 = 23x769231         (9.0s)
19: 19,173,071 = 19x19x173x307     (7.1s)
20: 28,118,827 = 11x11x281x827     (46.2s)
Total time:1 minute and 59s

Raku

<lang perl6>use Prime::Factor; use Lingua::EN::Numbers;

put (2..∞).hyper(:5000batch).map( {

   next if (1 < $_ gcd 210) || .is-prime || any .&prime-factors.map: -> $n { !.contains: $n };
   $_

} )[^20].batch(10)».&comma».fmt("%10s").join: "\n";</lang>

Output:

    15,317     59,177     83,731    119,911    183,347    192,413  1,819,231  2,111,317  2,237,411  3,129,361
 5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827

Wren

Library: Wren-math

<lang ecmascript>import "/math" for Int import "/fmt" for Fmt

var count = 0 var k = 11 var res = [] while (count < 20) {

   if (k % 3 == 0 || k % 5 == 0 || k % 7 == 0) {
       k = k + 2
       continue
   }
   var factors = Int.primeFactors(k)
   if (factors.count > 1) {
       var s = k.toString
       var includesAll = true
       for (f in factors) {
           if (s.indexOf(f.toString) == -1) {
               includesAll = false
               break
           }
       }
       if (includesAll) {
           res.add(k)
           count = count + 1
       }
   }
   k = k + 2

} Fmt.print("$,10d", res[0..9]) Fmt.print("$,10d", res[10..19])</lang>

Output:

    15,317     59,177     83,731    119,911    183,347    192,413  1,819,231  2,111,317  2,237,411  3,129,361
 5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827