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A147992 Sequence S such that 1 is in S and if x is in S, then 4x-1 and 4x+1 are in S. 9
1, 3, 5, 11, 13, 19, 21, 43, 45, 51, 53, 75, 77, 83, 85, 171, 173, 179, 181, 203, 205, 211, 213, 299, 301, 307, 309, 331, 333, 339, 341, 683, 685, 691, 693, 715, 717, 723, 725, 811, 813, 819, 821, 843, 845, 851, 853, 1195, 1197, 1203, 1205, 1227, 1229, 1235 (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

Gevorg Hmayakyan, Trig identity for a(n)

FORMULA

Product_{j=0..n-1} cos(4^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)/4^(n-1)*Pi/2) = 0. - Gevorg Hmayakyan, Jan 15 2017

EXAMPLE

0th generation: 1

1st generation: 3 5

2nd generation: 11 13 19 21

CROSSREFS

Sequence in context: A047621 A239636 A117205 * A166089 A136208 A045405

Adjacent sequences:  A147989 A147990 A147991 * A147993 A147994 A147995

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 07 2008

STATUS

approved

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Last modified June 25 10:10 EDT 2019. Contains 324351 sequences. (Running on oeis4.)