A147993 Sequence S such that 1 is in S and if x is in S, then 6x-1 and 6x+1 are in S.

1, 5, 7, 29, 31, 41, 43, 173, 175, 185, 187, 245, 247, 257, 259, 1037, 1039, 1049, 1051, 1109, 1111, 1121, 1123, 1469, 1471, 1481, 1483, 1541, 1543, 1553, 1555, 6221, 6223, 6233, 6235, 6293, 6295, 6305, 6307, 6653, 6655, 6665, 6667, 6725, 6727, 6737, 6739

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: 5 7
2nd generation: 29 31 41 43
		

Links

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

Crossrefs

Cf. A032806.

Column k=6 of A360099.

Programs

Mathematica

sss[n_]:={6n-1,6n+1}; NestList[Sort[Flatten[sss[#]]]&,{1},5]//Flatten (* Harvey P. Dale, Aug 06 2018 *)

Formula

Product_{j=0..n-1} cos(6^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)/6^(n-1))*(Pi/2)) = 0. - Gevorg Hmayakyan, Jan 15 2017

a(n) = 2*A032806(n-1) + 1 for n>=2. - Alois P. Heinz, Jan 29 2023