A126630 a(1)=1. a(n) = the number of earlier terms that are coprime to the n-th Fibonacci number.

1, 1, 2, 3, 4, 3, 6, 4, 4, 9, 10, 2, 12, 13, 6, 9, 16, 7, 18, 10, 7, 21, 22, 3, 22, 25, 12, 15, 28, 11, 30, 15, 15, 33, 26, 7, 36, 37, 19, 12, 40, 19, 42, 24, 17, 45, 46, 9, 46, 36, 24, 27, 52, 22, 45, 22, 25, 57, 58, 10, 60, 61, 27, 30, 50, 30, 66, 35, 31, 41, 70, 10, 72, 73, 25, 41

Offset

1,3

Links

Table of n, a(n) for n=1..76.

Example

The 8th Fibonacci number is 21. There are four terms from among the first 8 terms that are coprime to 21: a(1)=1, a(2)=1, a(3)=2 and a(5)=4. So a(8) = 4.

Maple

with(combinat): a:=proc(n) local ct, j: if n=1 then ct:=1: else ct:=0: for j from 1 to n-1 do if gcd(fibonacci(n), a(j))=1 then ct:=ct+1 else ct:=ct fi: od: fi: ct; end: seq(a(n), n=1..18); # Emeric Deutsch, Mar 23 2007

Mathematica

a = {1}; Do[AppendTo[a, Length[Select[a, GCD[ #, Fibonacci[Length[a] + 1]] == 1 &]]], {80}]; a (* Stefan Steinerberger, Oct 16 2007 *)

Crossrefs

Sequence in context: A117659 A079065 A097272 * A167234 A088043 A332931

Adjacent sequences: A126627 A126628 A126629 * A126631 A126632 A126633

Keyword

nonn

Author

Leroy Quet, Mar 13 2007

Extensions

More terms from Emeric Deutsch, Mar 23 2007

More terms from Stefan Steinerberger, Oct 16 2007

Status

approved