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

Author

Clark Kimberling, Dec 07 2008

Keywords

• nonn

Comments

Does every generation after the initial 1 contain a prime?

Examples

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

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Gevorg Hmayakyan, Trig identity for a(n)

Crossrefs

Cf. A032925.

Column k=4 of A360099.

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