A084909 Indices of Fibonacci numbers that satisfy: Sum_{k>=1} 1/F(a(k)) = tau-1, where F(k) gives the k-th Fibonacci number with F(0)=1, such that the partial sums are nearest to, but never exceed, tau-1 = (sqrt(5)-1)/2.

2, 6, 8, 10, 17, 21, 24, 26, 29, 34, 42, 46, 49, 51, 54, 56, 59, 61, 63, 65, 67, 69, 71, 77, 79, 81, 85, 88, 90, 92, 94, 101, 103, 110, 114, 121, 123, 129, 131, 134, 137, 143, 146, 149, 154, 156, 160, 163, 167, 172, 176, 181, 183, 185, 190, 193, 196, 199, 204, 206

Offset

1,1

Comments

Corresponding Fibonacci numbers are given by A084910.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

(sqrt(5)-1)/2 = 1/F(2) + 1/F(6) + 1/F(8) + 1/F(10) + 1/F(17) + 1/F(21) + ... = 1/2 + 1/13 + 1/34 + 1/89 + 1/2584 + 1/17711 + 1/75025 +...

Mathematica

seq = {}; s = GoldenRatio - 1; m = 3; Do[AppendTo[seq, m - 1]; s -= (1/Fibonacci[m]); While[Fibonacci[m] <= 1/s, m++], {60}]; seq (* Amiram Eldar, Nov 01 2019 *)

Prog

(PARI) x=(sqrt(5)-1)/2; a=2; S=0; for(n=1, 100, b=a+1; while(abs(S+1/fibonacci(b))>x, b++); S=S+1/fibonacci(b); a=b; print1(b-1, ", "))

Crossrefs

Cf. A000045, A001622, A084907, A084910.

Sequence in context: A302658 A324175 A358428 * A038619 A118257 A066762

Adjacent sequences: A084906 A084907 A084908 * A084910 A084911 A084912

Keyword

nonn

Author

Paul D. Hanna, Jun 10 2003

Status

approved