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

Author

Clark Kimberling

Keywords

• sign

Examples

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

Crossrefs

Cf. A054083, A054084.

Programs

Mathematica

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 *)

Extensions

Data truncated by Sean A. Irvine, Jan 23 2022

Edited by Clark Kimberling, Jan 26 2022