1,2

{a(n)} gives all positive fourth powers modulo all powers of 2, that is, positive fourth powers over 2-adic integers. So this sequence is closed under multiplication.

Jianing Song, Table of n, a(n) for n = 1..10002 (all terms <= 150000)

a(n) = 15*n + O(log(n)).

(PARI) isA319281(n)= n\16^valuation(n, 16)%16==1

A158057 is a proper subsequence.

Perfect powers over 2-adic integers:

Squares: positive: A234000; negative: A004215 (negated);

Cubes: A191257;

Fourth powers: positive: this sequence; negative: A319282 (negated).

Sequence in context: A244431 A151977 A252492 * A022106 A041518 A042195

Adjacent sequences: A319278 A319279 A319280 * A319282 A319283 A319284

nonn

Jianing Song, Sep 16 2018

approved