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

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

Example

0th generation: 1
1st generation: 3 5
2nd generation: 11 13 19 21

Crossrefs

Cf. A032925.

Column k=4 of A360099.

Sequence in context: A047621 A239636 A117205 * A166089 A136208 A045405

Adjacent sequences: A147989 A147990 A147991 * A147993 A147994 A147995

Keyword

nonn

Author

Clark Kimberling, Dec 07 2008

Status

approved