A147992 - OEIS

A147992

Sequence S such that 1 is in S and if x is in S, then 4x-1 and 4x+1 are in S.

1, 3, 5, 11, 13, 19, 21, 43, 45, 51, 53, 75, 77, 83, 85, 171, 173, 179, 181, 203, 205, 211, 213, 299, 301, 307, 309, 331, 333, 339, 341, 683, 685, 691, 693, 715, 717, 723, 725, 811, 813, 819, 821, 843, 845, 851, 853, 1195, 1197, 1203, 1205, 1227, 1229, 1235

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OFFSET

1,2

COMMENTS

Does every generation after the initial 1 contain a prime?

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

Gevorg Hmayakyan, Trig identity for a(n)

FORMULA

Product_{j=0..n-1} cos(4^j) = 2^(-n+1)*Sum_{i=2^(n-1)..2^n-1} cos(a(i)). - Gevorg Hmayakyan, Jan 15 2017

Sum_{i=2^(n-1)..2^n-1} cos(a(i)/4^(n-1)*Pi/2) = 0. - Gevorg Hmayakyan, Jan 15 2017

a(n) = 2*A032925(n-1) + 1 for n>=2. - Alois P. Heinz, Jan 29 2023