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
containsitsonlytwodigfactors(n) = (s = string(n); !isprime(n) && all(t -> length(t) > 1 && contains(s, t), map(x -> string(x), collect(keys(factor(n))))))
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
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 }; $_
} )[^20].batch(10)».&comma».fmt("%10s").join: "\n";</lang>
- Output:
15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361 5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827
Wren
<lang ecmascript>import "/math" for Int import "/fmt" for Fmt
var count = 0 var k = 11 var res = [] while (count < 20) {
if (k % 3 == 0 || k % 5 == 0 || k % 7 == 0) { k = k + 2 continue } var factors = Int.primeFactors(k) if (factors.count > 1) { var s = k.toString var includesAll = true for (f in factors) { if (s.indexOf(f.toString) == -1) { includesAll = false break } } if (includesAll) { res.add(k) count = count + 1 } } k = k + 2
} Fmt.print("$,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