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A293313
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Greatest integer k such that k/2^n < (1+sqrt(5))/2 (the golden ratio).
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8
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = floor(r*2^n), where r = (1+sqrt(5))/2.
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MAPLE
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MATHEMATICA
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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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PROG
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(PARI) a(n) = (2^n*(1+sqrt(5)))\2; \\ Altug Alkan, Oct 06 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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