A391519 - OEIS

%I #15 Dec 30 2025 23:31:18

%S 15625,117649,65477433301

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

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

%C The following are also terms:

%C      1076774322134762161 = 32213^4,

%C      7050287992278341281 = 227^8,

%C     18080443257103575743 = 7103^5,

%C   9444732965739290427392 = 2^73.

%C 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]

%e 15625 is a term since 15625 = 5^6 and 56 is a substring of 15626.

%e 117649 is a term since 117649 = 7^6 and 76 is a substring of 117649.

%e 65477433301 is a term since 65477433301 = 7^7 * 43^3 and 77433 is a substring of 65477433301.

%o (Python)

%o from sympy import factorint, isprime

%o def ok(n): return n > 1 and "".join(str(p)+str(e) for p, e in factorint(n).items()) in str(n)

%o print([k for k in range(10**6) if ok(k)])

%Y Cf. A067599, A027746, A390475, A378893.

%K nonn,more,base

%O 1,1

%A _Scott R. Shannon_ and _Michael S. Branicky_, Dec 12 2025