A128332 a(0)=a(1)=1. For n >= 2, a(n) = number of positive numbers <= n that are coprime to a(n-1) + a(n-2).

1, 1, 1, 2, 3, 4, 6, 3, 6, 6, 3, 8, 11, 13, 5, 5, 6, 16, 8, 7, 11, 7, 7, 10, 23, 15, 12, 18, 7, 24, 30, 11, 32, 33, 26, 35, 36, 37, 38, 21, 40, 41, 28, 28, 19, 45, 23, 23, 23, 24, 49, 51, 21, 18, 33, 35, 26, 57, 58, 46, 28, 30, 30, 17, 63, 26, 66, 33, 42, 37, 70, 71, 47, 36, 74, 28

Offset

0,4

Links

Ivan Neretin, Table of n, a(n) for n = 0..10000

Example

a(5) + a(6) = 10. The number of positive integers <= 7 that are coprime to 10 is three, these integers being 1, 3 and 7. So a(7) = 3.

Maple

a[0]:=1: a[1]:=1: for n from 2 to 100 do ct:=0: for j from 1 to n do if igcd(j, a[n-1]+a[n-2])=1 then ct:=ct+1 else fi od: a[n]:=ct: od: seq(a[n], n=0..100); # Emeric Deutsch, May 07 2007

Mathematica

nxt[{n_, a_, b_}]:={n+1, b, Count[Range[n+1], _?(CoprimeQ[a+b, #]&)]}; Transpose[ NestList[ nxt, {1, 1, 1}, 80]][[2]] (* Harvey P. Dale, Jan 21 2015 *)

Crossrefs

Cf. A000010 (number of positive numbers <= n that are coprime to n).

Sequence in context: A260272 A377993 A321479 * A074103 A051785 A144825

Adjacent sequences: A128329 A128330 A128331 * A128333 A128334 A128335

Keyword

nonn

Author

Leroy Quet, May 04 2007

Extensions

More terms from Emeric Deutsch, May 07 2007

Status

approved