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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

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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

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