A054085 - OEIS

A054085

a(n) = order of 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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..69.

EXAMPLE

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

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,