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A319281 Numbers of the form 16^i*(16*j + 1). 3


%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

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Last modified November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)