A064157 Primes p such that (x1*x2*...*xk)^(x1+x2+...+xk) = (x1+x2+...+xk)^(x1*x2*...*xk) where x1x2...xk are the digits of p in base 10.

2, 3, 5, 7, 211, 2141, 2411, 4211, 11251, 12511, 15121, 21221, 25111, 1112171, 1127111, 1172111, 1271111, 7112111, 11112811, 11128111, 11218111, 12111811, 12118111, 12181111, 18211111, 81111211, 81112111, 1111411141, 4111111141, 4111411111, 11111112421, 11111124121

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = A066306(n-1) for n > 5. - Jinyuan Wang, Sep 08 2025

Example

211 belongs to the sequence because (2*1*1)^(2+1+1) = (2+1+1)^(2*1*1).

Crossrefs

Intersection of A000040 and A064158.

Supersequence of A066306.

Sequence in context: A122764 A256886 A195302 * A257483 A178371 A067184

Adjacent sequences: A064154 A064155 A064156 * A064158 A064159 A064160

Keyword

nonn,base

Author

Felice Russo, Sep 14 2001

Extensions

More terms from Jason Earls, Dec 05 2001

a(18)-a(30) from Sean A. Irvine, Jun 16 2023

a(31)-a(32) from Jinyuan Wang, Sep 08 2025

Status

approved