A054084 -id:A054084 - cp's OEIS frontend

A054085 a(n) = order of n in the permutation A054084 of the natural numbers if this order exists; a(n) = -1 otherwise.

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, -1

Offset: 1

Clark Kimberling

sign

			3 -> 5 -> 7 -> 10 -> 8 -> 6 -> 4 -> 3, so that 3 has order 7.

Cf. A054083, A054084.

a054084[n_] := a054084[n] = If[EvenQ[n], Floor[n/2*GoldenRatio],
Floor[(n + 1)/2*GoldenRatio^2]];
Array[a054084[#] &, 40]  (* after Jean-François Alcover *)
Table[Length[NestWhileList[a054084, a054084[n], # != n &, 1,
     10000]] /. (10001 -> -1), {n, 1, 500}]
(* Peter J. C. Moses, Jan 26 2022 *)

Data truncated by Sean A. Irvine, Jan 23 2022

Edited by Clark Kimberling, Jan 26 2022

A064786 Inverse permutation to A054084.

Original entry on oeis.org

2, 1, 4, 6, 3, 8, 5, 10, 12, 7, 14, 16, 9, 18, 11, 20, 22, 13, 24, 15, 26, 28, 17, 30, 32, 19, 34, 21, 36, 38, 23, 40, 42, 25, 44, 27, 46, 48, 29, 50, 31, 52, 54, 33, 56, 58, 35, 60, 37, 62, 64, 39, 66, 41, 68, 70, 43, 72, 74, 45, 76, 47, 78, 80, 49, 82, 84, 51, 86, 53, 88, 90

Offset: 1

N. J. A. Sloane, Oct 20 2001

Index entries for sequences that are permutations of the natural numbers

More terms from Vladeta Jovovic, Oct 22 2001

cp's OEIS Frontend

A054085 a(n) = order of n in the permutation A054084 of the natural numbers if this order exists; a(n) = -1 otherwise.

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A064786 Inverse permutation to A054084.

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