A343184 Positions of records in A001178.

1, 2, 127, 509, 1019, 2039, 4079, 16384, 32768, 65536, 131072, 262144, 524287, 1048573, 6291437

Offset

1,2

Comments

When the Pisano-period map x -> A001175(x) is iterated, a(n) is the number of steps needed to reach a fixed point (that is, to reach a term of A235702).

The record values of A001178 at positions 1, 2, 127, 509, 1019, 2039, 4079, 16384, 32768, 65536, 131072, 262144, 524287, 1048573 are 0, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19.

Felix Lans remarks that from a(4) onwards, the terms appear to be very close to consecutive powers of 2, except that there is no term close to 2^13.

Links

Table of n, a(n) for n=1..15.

Mathematica

Block[{pi, k, s}, pi[1] = 1; pi[n_] := For[k = 1, True, k++, If[Mod[Fibonacci[k], n] == 0 && Mod[Fibonacci[k + 1], n] == 1, Return[k]]]; s = Array[Length[FixedPointList[pi, #]] - 2 &, 2^11]; Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] ] (* Michael De Vlieger, May 16 2021, after Jean-François Alcover at A001178  *)

Crossrefs

Cf. A001175, A001178, A235702.

Sequence in context: A065381 A274123 A141928 * A062588 A125634 A075596

Adjacent sequences: A343181 A343182 A343183 * A343185 A343186 A343187

Keyword

nonn,more

Author

N. J. A. Sloane, May 16 2021, following an email from Felix Lans

Extensions

a(1)-a(12) from Felix Lans and confirmed by Rémy Sigrist, May 16 2021; a(13) and a(14) from Rémy Sigrist, May 16 2021.

a(15) from Chai Wah Wu, Mar 01 2022

Status

approved