A390475 - OEIS

%I #49 Jan 10 2026 19:49:47

%S 15,232,1111,1131,3171,7112,8571,11110,11371,17119,22564,31291,37127,

%T 53159,131131,190911,317169,1283122,1712914,3141133,5131120,11101112,

%U 12711811,14713491,19090911,19114912,31311891,35911069,71119711,99119863,171111171,233451720

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

%C The property is trivially true if k is a prime.

%C [Needs a b-file! - _N. J. A. Sloane_, Dec 30 2025]

%H Scott R. Shannon, <a href="/A390475/b390475.txt">Table of n, a(n) for n = 1..41</a>

%e 15 is a term since 15 = 3^1 * 5^1 and 15 is a substring of 3151.

%e 1131 is a term since 1131 = 3^1 * 13^1 * 29^1 and 1131 is a substring of 31131291.

%e 22564 is a term since 22564 = 2^2 * 5641^1 and 22564 is a substring of 2256411.

%t 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 *)

%o (Python)

%o from sympy import factorint, isprime

%o 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())

%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Dec 11 2025

%o (PARI) f(n) = eval(concat(concat([""], concat(Vec(factor(n)~))~))); \\ A067599

%o isok(k) = #strsplit(Str(f(k)), Str(k)) >=2;

%o forcomposite (n=2, 10^7, if (isok(n), print1(n, ", "))) \\ _Michel Marcus_, Dec 31 2025

%Y Cf. A067599, A027746, A391519, A378893.

%K nonn,base

%O 1,1

%A _Scott R. Shannon_, Dec 10 2025