A390475 Composite numbers k such that k is a substring of A067599(k).

15, 232, 1111, 1131, 3171, 7112, 8571, 11110, 11371, 17119, 22564, 31291, 37127, 53159, 131131, 190911, 317169, 1283122, 1712914, 3141133, 5131120, 11101112, 12711811, 14713491, 19090911, 19114912, 31311891, 35911069, 71119711, 99119863, 171111171, 233451720

Offset

1,1

Comments

The property is trivially true if k is a prime.

[Needs a b-file! - N. J. A. Sloane, Dec 30 2025]

Links

Scott R. Shannon, Table of n, a(n) for n = 1..41

Example

15 is a term since 15 = 3^1 * 5^1 and 15 is a substring of 3151.
1131 is a term since 1131 = 3^1 * 13^1 * 29^1 and 1131 is a substring of 31131291.
22564 is a term since 22564 = 2^2 * 5641^1 and 22564 is a substring of 2256411.

Mathematica

Select[Range[2*10^6], CompositeQ[#]&&SequenceCount[Flatten[IntegerDigits/@Flatten[FactorInteger[#]]], IntegerDigits[#]]>0&] (* The program generates the first 19 terms of the sequence. *) (* Harvey P. Dale, Jan 10 2026 *)

Prog

(Python)
from sympy import factorint, isprime
def ok(n): return n and not isprime(n) and str(n) in "".join(str(p)+str(e) for p, e in factorint(n).items())
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Dec 11 2025
(PARI) f(n) = eval(concat(concat([""], concat(Vec(factor(n)~))~))); \\ A067599
isok(k) = #strsplit(Str(f(k)), Str(k)) >=2;
forcomposite (n=2, 10^7, if (isok(n), print1(n, ", "))) \\ Michel Marcus, Dec 31 2025

Crossrefs

Cf. A067599, A027746, A391519, A378893.

Sequence in context: A075262 A286722 A250418 * A231411 A097185 A372195

Adjacent sequences: A390472 A390473 A390474 * A390476 A390477 A390478

Keyword

nonn,base

Author

Scott R. Shannon, Dec 10 2025

Status

approved