A084908 Fibonacci numbers that satisfy: Sum_{k>=1} 1/a(k) = 1, such that the partial sums are nearest to, but never exceed, unity.

2, 3, 8, 34, 89, 987, 196418, 2178309, 5702887, 24157817, 165580141, 433494437, 4807526976, 12586269025, 32951280099, 86267571272, 365435296162, 956722026041, 4052739537881, 8944394323791464, 23416728348467685

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