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

1, 16, 17, 33, 49, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 256, 257, 272, 273, 289, 305, 321, 337, 353, 369, 385, 401, 417, 433, 449, 465, 481, 497, 513, 528, 529, 545, 561, 577, 593, 609, 625, 641, 657, 673, 689, 705, 721, 737, 753, 769, 784

Offset

1,2

Comments

{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.

Links

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

Formula

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

Prog

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

Crossrefs

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

Keyword

nonn

Author

Jianing Song, Sep 16 2018

Status

approved