A391519 Numbers k such that A067599(k) is a substring of k.

15625, 117649, 65477433301

Offset

1,1

Comments

a(4) <= 2251799813685248 = 2^51.

The following are also terms:

1076774322134762161 = 32213^4,

7050287992278341281 = 227^8,

18080443257103575743 = 7103^5,

9444732965739290427392 = 2^73.

It is easy to generate larger terms by searching for cases where the string p|e is contained in the digits of p^e, where | denotes concatenation. [Of course this does not mean they are the next terms in the sequence, since there are other ways that terms can be created. - N. J. A. Sloane, Dec 30 2025]

Links

Table of n, a(n) for n=1..3.

Example

15625 is a term since 15625 = 5^6 and 56 is a substring of 15626.
117649 is a term since 117649 = 7^6 and 76 is a substring of 117649.
65477433301 is a term since 65477433301 = 7^7 * 43^3 and 77433 is a substring of 65477433301.

Prog

(Python)
from sympy import factorint, isprime
def ok(n): return n > 1 and "".join(str(p)+str(e) for p, e in factorint(n).items()) in str(n)
print([k for k in range(10**6) if ok(k)])

Crossrefs

Cf. A067599, A027746, A390475, A378893.

Sequence in context: A129152 A223185 A097219 * A016818 A016854 A016974

Adjacent sequences: A391516 A391517 A391518 * A391520 A391521 A391522

Keyword

nonn,more,base

Author

Scott R. Shannon and Michael S. Branicky, Dec 12 2025

Status

approved