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A084908 Fibonacci numbers that satisfy: Sum_{k>=1} 1/a(k)) = 1, such that the partial sums are nearest to, but never exceed, unity. 3
2, 3, 8, 34, 89, 987, 196418, 2178309, 5702887, 24157817, 165580141, 433494437, 4807526976, 12586269025, 32951280099, 86267571272, 365435296162, 956722026041, 4052739537881, 8944394323791464, 23416728348467685 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Corresponding Fibonacci indices are given by A084907.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1332

FORMULA

a(n) = A000045(A084907(n)+1). - Amiram Eldar, Nov 01 2019

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

CROSSREFS

Cf. A000045, A084907, A084910.

Sequence in context: A162052 A082569 A340495 * A078742 A005370 A112866

Adjacent sequences:  A084905 A084906 A084907 * A084909 A084910 A084911

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 10 2003

STATUS

approved

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Last modified January 16 09:13 EST 2021. Contains 340204 sequences. (Running on oeis4.)