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 A054083 a(n) = order of in the permutation A054082 of the natural numbers if this order exists; a(n) = -1 otherwise. 1
 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 9, 7, 9, 9, 9, 9, 9, 9, -1, 9, -1, 9, -1, -1, -1, -1, 16, -1, 16, -1, 16, -1, -1, 16, 16, 16, 16, 16, -1, -1, 16, 16, -1, 16, -1, 16, -1, -1, 16, -1, -1, 16, -1, 16, -1, -1, -1, -1, -1, -1, -1, -1, -1, 16, -1, -1, -1, -1, -1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Peter J. C. Moses, Jan 26 2022: (Start) For n up to 60000, a(n) = 2 for n = 1, 2, 3, 4; a(n) = 7 for n = 5, 6, 7, 8, 9, 10, 12 a(n) = 9 for n = 11, 13, 14, 15, 16, 17, 18, 20, 22 a(n) = 16 for n = 27, 29, 31, 34, 35, 36, 37, 38, 41, 42, 44, 46, 49, 52, 54, 64 a(n) = 25 for n = 267, 283, 330, 343, 350, 371, 385, 393, 408, 424, 449, 467, 476, 486, 495, 504, 515, 524, 545, 578, 588, 612, 648, 674, 714. (End) LINKS Table of n, a(n) for n=1..70. EXAMPLE 5 -> 7 -> 9 -> 12 -> 10 -> 8-> 6-> 5, so that 5 has order 7. MATHEMATICA a054082[n_] := a054082[n] = If[OddQ[n], Floor[((n + 1)/2 - 1) GoldenRatio] + (n + 1)/2 + 1, Floor[(n/2 - 1) GoldenRatio] + 2]; a054082[2] = 1; Array[a054082[#] &, 40] (* after Jean-François Alcover *) Table[Length[NestWhileList[a054082, a054082[n], # != n &, 1, 10000]] /. (10001 -> -1), {n, 1, 500}] (* Peter J. C. Moses, Jan 26 2022 *) CROSSREFS Cf. A054082, A054085. Sequence in context: A061292 A138068 A246052 * A270379 A337358 A295557 Adjacent sequences: A054080 A054081 A054082 * A054084 A054085 A054086 KEYWORD sign AUTHOR Clark Kimberling EXTENSIONS Data truncated by Sean A. Irvine, Jan 23 2022 Edited by Clark Kimberling, Jan 26 2022 STATUS approved

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Last modified May 21 21:53 EDT 2024. Contains 372738 sequences. (Running on oeis4.)