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

1,2

Comments

Does every generation after the initial 1 contain a prime?

Links

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

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

Example

0th generation: 1
1st generation: 5 7
2nd generation: 29 31 41 43

Mathematica

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

Crossrefs

Cf. A032806.

Column k=6 of A360099.

Sequence in context: A229337 A227857 A266078 * A213901 A087901 A018776

Adjacent sequences: A147990 A147991 A147992 * A147994 A147995 A147996

Keyword

nonn

Author

Clark Kimberling, Dec 07 2008

Status

approved