A084910 Fibonacci numbers that satisfy: Sum_{k>=1} 1/a(k) = tau-1, such that the partial sums are nearest to, but never exceed, tau-1 = (sqrt(5)-1)/2.

2, 13, 34, 89, 2584, 17711, 75025, 196418, 832040, 9227465, 433494437, 2971215073, 12586269025, 32951280099, 139583862445, 365435296162, 1548008755920, 4052739537881, 10610209857723, 27777890035288, 72723460248141

Offset

1,1

Comments

Corresponding Fibonacci indices are given by A084909.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1323

Formula

a(n) = A000045(A084909(n)+1). - Amiram Eldar, Nov 01 2019

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, Fibonacci[m]]; s -= (1/Fibonacci[m]); While[Fibonacci[m] <= 1/s, m++], {21}]; 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(fibonacci(b), ", "))

Crossrefs

Cf. A000045, A001622, A084908, A084909.

Sequence in context: A062708 A296293 A190816 * A124024 A102229 A254965

Adjacent sequences: A084907 A084908 A084909 * A084911 A084912 A084913

Keyword

nonn

Author

Paul D. Hanna, Jun 10 2003

Status

approved