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 A330117 Beatty sequence for 1+x, where 1/(1+x) + 1/(1+x+x^2) = 1. 2
 1, 3, 5, 7, 8, 10, 12, 14, 15, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 35, 36, 38, 40, 42, 43, 45, 47, 49, 50, 52, 54, 56, 57, 59, 61, 63, 64, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 107, 108, 110, 112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let x be the positive solution of 1/(1+x) + 1/(1+x+x^2) = 1. Then (floor(n*(1+x)) and (floor(n*(1+x+x^2))) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825. LINKS Eric Weisstein's World of Mathematics, Beatty Sequence. FORMULA a(n) = floor(n (1+x))), where x = 0.7548776662... is the constant in A3075778. MATHEMATICA r = x /. FindRoot[1/(1 + x) + 1/(1 + x + x^2) == 1, {x, 1, 2}, WorkingPrecision -> 200] RealDigits[r] (* A075778 *) Table[Floor[n*(1 + r)], {n, 1, 250}]  (* A330117 *) Table[Floor[n*(1 + r + r^2)], {n, 1, 250}]  (* A330118 *) Plot[1/(1 + x) + 1/(1 + x + x^2) - 1, {x, 0, 2}] CROSSREFS Cf. A329825, A075778, A330118 (complement). Sequence in context: A144077 A184626 A047392 * A292648 A187330 A059546 Adjacent sequences:  A330114 A330115 A330116 * A330118 A330119 A330120 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jan 04 2020 STATUS approved

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Last modified June 1 07:40 EDT 2020. Contains 334759 sequences. (Running on oeis4.)