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A084907 Indices of Fibonacci numbers that satisfy: Sum_{k>=1} 1/F(a(k))) = 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, unity. 3
2, 3, 5, 8, 10, 15, 26, 31, 33, 36, 40, 42, 47, 49, 51, 53, 56, 58, 61, 77, 79, 81, 84, 88, 90, 92, 95, 97, 99, 102, 104, 106, 111, 113, 115, 120, 122, 127, 129, 132, 136, 138, 141, 145, 147, 150, 157, 159, 162, 164, 172, 177, 181, 183, 185, 200, 203, 206, 209, 211 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Corresponding Fibonacci numbers are given by A084908.

LINKS

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

EXAMPLE

1 = 1/F(2) + 1/F(3) + 1/F(5) + 1/F(8) + 1/F(10) + 1/F(15) + ... = 1/2 + 1/3 + 1/8 + 1/34 + 1/89 + 1/987 + 1/196418 + 1/2178309 +...

MATHEMATICA

seq = {}; s = 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=1; 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, A084908, A084909.

Sequence in context: A306972 A087279 A246346 * A158724 A289276 A181100

Adjacent sequences:  A084904 A084905 A084906 * A084908 A084909 A084910

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 10 2003

EXTENSIONS

Terms a(41) onward corrected by Amiram Eldar, Nov 01 2019

STATUS

approved

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Last modified March 5 16:55 EST 2021. Contains 341827 sequences. (Running on oeis4.)