A129989 a(1)=1. a(n) = smallest integer > a(n-1) that is coprime to the n-th Fibonacci number.

1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 17, 18, 19, 21, 22, 23, 25, 26, 28, 29, 30, 31, 37, 38, 39, 41, 43, 44, 47, 48, 50, 51, 52, 53, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 82, 83, 84, 85, 89, 90, 91

Offset

1,2

Links

Table of n, a(n) for n=1..62.

Example

The 12th Fibonacci number is 144. So a(12) is the smallest positive integer greater than a(11) (a(11)=13) which is coprime to 144. So a(12) = 17.

Mathematica

a={1}; For[n=2, n<90, n++, k=a[[ -1]]+1; While[ !GCD[Fibonacci[n], k]==1, k++ ]; AppendTo[a, k]]; a (* Stefan Steinerberger, Jun 16 2007 *)
cpf[n_, a_]:=Module[{f=Fibonacci[n+1], k=a+1}, While[!CoprimeQ[f, k], k++]; k]; nxt[{n_, a_}] := {n + 1, cpf[n, a]}; Transpose[NestList[nxt, {1, 1}, 70]][[2]] (* Harvey P. Dale, Feb 06 2015 *)

Crossrefs

Sequence in context: A039081 A195128 A119931 * A187572 A184478 A188188

Adjacent sequences: A129986 A129987 A129988 * A129990 A129991 A129992

Keyword

nonn

Author

Leroy Quet, Jun 14 2007

Extensions

More terms from Stefan Steinerberger, Jun 16 2007

Status

approved