

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

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



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 JeanFrançois Alcover *)
Table[Length[NestWhileList[a054082, a054082[n], # != n &, 1,
10000]] /. (10001 > 1), {n, 1, 500}]


CROSSREFS



KEYWORD

sign


AUTHOR



EXTENSIONS



STATUS

approved



