%I
%S 1,16,17,33,49,65,81,97,113,129,145,161,177,193,209,225,241,256,257,
%T 272,273,289,305,321,337,353,369,385,401,417,433,449,465,481,497,513,
%U 528,529,545,561,577,593,609,625,641,657,673,689,705,721,737,753,769,784
%N Numbers of the form 16^i*(16*j + 1).
%C {a(n)} gives all positive fourth powers modulo all powers of 2, that is, positive fourth powers over 2adic integers. So this sequence is closed under multiplication.
%H Jianing Song, <a href="/A319281/b319281.txt">Table of n, a(n) for n = 1..10002</a> (all terms <= 150000)
%F a(n) = 15*n + O(log(n)).
%o (PARI) isA319281(n)= n\16^valuation(n, 16)%16==1
%Y A158057 is a proper subsequence.
%Y Perfect powers over 2adic integers:
%Y Squares: positive: A234000; negative: A004215 (negated);
%Y Cubes: A191257;
%Y Fourth powers: positive: this sequence; negative: A319282 (negated).
%K nonn
%O 1,2
%A _Jianing Song_, Sep 16 2018
