2,1

Probably infinite.

All the terms are of the form b^(y/2), where b is any of 2..n and where y is any odd number greater than 1. (See the link for proof.)

It is suspected that terms of the form (n+1)^z could exist, where z is any integer greater than 0.

Jakub Buczak, A guide to A392007

a(4) = 47, because 47 is the smallest number k for which the inequality log_b(47) - ceiling(log_b(47)) >= 1/2 holds for b = 2,3,4 and not for b=5.

Cf. A020857, A153459.

Cf. A002193, A002194, A002163, A010464.

Sequence in context: A038050 A194080 A261841 * A197884 A279706 A032322

Adjacent sequences: A392004 A392005 A392006 * A392008 A392009 A392010

nonn,more

Jakub Buczak, Dec 26 2025

approved