Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Sep 17 2018 15:44:34
%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 2-adic 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 2-adic 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