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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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

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

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)