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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.
11
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
OFFSET
1,2
COMMENTS
Does every generation after the initial 1 contain a prime?
LINKS
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
a(n) = 2*A032925(n-1) + 1 for n>=2. - Alois P. Heinz, Jan 29 2023
EXAMPLE
0th generation: 1
1st generation: 3 5
2nd generation: 11 13 19 21
CROSSREFS
Cf. A032925.
Column k=4 of A360099.
Sequence in context: A047621 A239636 A117205 * A166089 A136208 A045405
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 07 2008
STATUS
approved