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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.
9
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 07 2008
STATUS
approved