A218872 Numerator of Sum_{i = Fibonacci(n-1)+1..Fibonacci(n)} 1/i.

1, 0, 1, 1, 9, 73, 11899, 757349, 3593758191731, 43428537271777524533, 19697237980702493347945111637368211, 41621642499053452254184404257646193170072171058019663

Offset

1,5

Links

Amiram Eldar, Table of n, a(n) for n = 1..18

Hongwei Chen and Chris Kennedy, Harmonic series meets Fibonacci sequence, College Math. J., Vol. 43, No. 3 (2012), 237-243. MR2916493.

Formula

Limit_{n->oo} a(n)/A218873(n) = log(phi) = A002390, where phi is the golden ratio (A001622). - Amiram Eldar, Jul 07 2026

Example

1, 0, 1/2, 1/3, 9/20, 73/168, 11899/25740, 757349/1627920, 3593758191731/7600186994400, 43428537271777524533/91351145008363640400, ...

Mathematica

a[n_] := Numerator[Sum[1/i, {i, Fibonacci[n-1]+1, Fibonacci[n]}]]; Array[a, 13] (* Amiram Eldar, Jul 07 2026 *)

Crossrefs

Cf. A000045, A001008, A002805, A218873 (denominators).

Cf. A001622, A002390.

Sequence in context: A197534 A015465 A144782 * A075232 A145524 A319961

Adjacent sequences: A218869 A218870 A218871 * A218873 A218874 A218875

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 09 2012

Status

approved