A293313 Greatest integer k such that k/2^n < (1+sqrt(5))/2 (the golden ratio).
1, 3, 6, 12, 25, 51, 103, 207, 414, 828, 1656, 3313, 6627, 13254, 26509, 53019, 106039, 212078, 424157, 848315, 1696631, 3393263, 6786526, 13573052, 27146105, 54292211, 108584422, 217168845, 434337691, 868675383, 1737350766, 3474701532, 6949403065
Offset: 0
Links
- Clark Kimberling, Table of n, a(n) for n = 0..1000
Programs
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Maple
A293313:=n->floor(2^n*(1+sqrt(5))/2): seq(A293313(n), n=0..40); # Wesley Ivan Hurt, Oct 06 2017
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Mathematica
z = 120; r = GoldenRatio; Table[Floor[r*2^n], {n, 0, z}]; (* A293313 *) Table[Ceiling[r*2^n], {n, 0, z}]; (* A293314 *) Table[Round[r*2^n], {n, 0, z}]; (* A293315 *)
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PARI
a(n) = (2^n*(1+sqrt(5)))\2; \\ Altug Alkan, Oct 06 2017
Formula
a(n) = floor(r*2^n), where r = (1+sqrt(5))/2.
a(n) = A293314(n) - 1.