A160757 Averages of the Fibonacci numbers which take integer values.

1, 1, 5058, 262213938, 18124577012898, 187952389930860, 1409394295257361938, 116903055445824294157698, 10100618828005365858877129458, 81435914480042681825934186407384633298, 7505278652741640947693896415563573183203138, 700346071081054203480884565881868806176873272498

Offset: 1

Author

Daniel Tisdale, May 25 2009

Keywords

• easy
• nonn

Comments

The numbers n such that F(1)+F(2)+...+F(n)=F(n+2)-1 is divisible by n are given in A111035. [From Max Alekseyev, Jun 04 2009]

Crossrefs

Cf. A050248, integer average of n primes for some n, A000045.

Programs

Mathematica

lst = {}; Do[a = Sum[ Fibonacci@ j, {j, n}]/n; If[ IntegerQ@ a, AppendTo[lst, a]], {n, 250}]; lst

Formula

1/n*Sum {j=1..n} Fibonacci_j is an integer.

a(n) = (A000045(A111035(n)+2)-1) / A111035(n) = A000071(A111035(n)+2) / A111035(n) [From Max Alekseyev, Jun 04 2009]

Extensions

Corrected and extended by Max Alekseyev and Robert G. Wilson v, Jun 04 2009