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 A293313 Greatest integer k such that k/2^n < (1+sqrt(5))/2 (the golden ratio). 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 FORMULA a(n) = floor(r*2^n), where r = (1+sqrt(5))/2. a(n) = A293314(n) - 1. MAPLE A293313:=n->floor(2^n*(1+sqrt(5))/2): seq(A293313(n), n=0..40); # Wesley Ivan Hurt, Oct 06 2017 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 *) PROG (PARI) a(n) = (2^n*(1+sqrt(5)))\2; \\ Altug Alkan, Oct 06 2017 CROSSREFS Cf. A001622, A293314, A293315. Sequence in context: A136444 A077854 A265700 * A267539 A243722 A187260 Adjacent sequences: A293310 A293311 A293312 * A293314 A293315 A293316 KEYWORD nonn,easy AUTHOR Clark Kimberling, Oct 06 2017 STATUS approved

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Last modified February 28 16:50 EST 2024. Contains 370400 sequences. (Running on oeis4.)