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 A329847 Beatty sequence for (3+sqrt(89))/8. 3
 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 87, 88, 90, 91, 93, 94, 96, 97, 99, 101, 102 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let r = (3+sqrt(89))/8. Then (floor(n*r)) and (floor(n*r + 5r/4)) 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*r), where r = (3+sqrt(89))/8. MATHEMATICA t = 5/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)]; Table[Floor[r*n], {n, 1, 200}]   (* A329847 *) Table[Floor[s*n], {n, 1, 200}]   (* A329848 *) CROSSREFS Cf. A329825, A329848 (complement). Sequence in context: A226901 A286323 A059559 * A103877 A072561 A330176 Adjacent sequences:  A329844 A329845 A329846 * A329848 A329849 A329850 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jan 02 2020 STATUS approved

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Last modified June 24 21:09 EDT 2021. Contains 345425 sequences. (Running on oeis4.)