OFFSET
1,2
COMMENTS
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Y. Bugeaud, F. Luca, M. Mignotte and S. Siksek, On Fibonacci numbers with few prime divisors, Proc. Japan Acad., 81, Ser. A (2005), pp. 17-20.
H. R. Morton, Fibonacci-like sequences and greatest common divisors, The American Mathematical Monthly, Vol. 102, No. 8 (October 1995), pp. 731-734.
M. Ward, The prime divisors of Fibonacci numbers, Pacific J. Math., Vol. 11, No. 1 (1961), pp. 379-386.
Eric W. Weisstein's World of Mathematics, Arithmetic mean
Eric W. Weisstein's World of Mathematics, Fibonacci
FORMULA
Numbers n-1 such that (F(0)+ F(1)+ ... + F(n-1)) / n is an integer. F(i) is the i-th Fibonacci number.
a(n) = A219612(n) - 1. - Altug Alkan, Dec 29 2015
EXAMPLE
n=4 : (F(0)+F(1)+F(2)+F(3))/4 = (0+1+1+2)/4 = 1. So n-1 = 4-1 = 3 is a term.
n=6 : (F(0)+F(1)+F(2)+F(3)+F(4)+F(5))/6 = (0+1+1+2+3+5)/6 = 2. So n-1 = 6-1 = 5 is a term.
MATHEMATICA
Select[ Range[0, 500], Mod[Fibonacci[ # + 2] - 1, # + 1] == 0 &] (* Robert G. Wilson v *)
PROG
(PARI) is(n)=((Mod([1, 1; 1, 0], n+1))^(n+2))[1, 2]==1 \\ Charles R Greathouse IV, Feb 04 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Jul 27 2008
EXTENSIONS
Edited and extended by Robert G. Wilson v, Aug 03 2008
Definition corrected by Altug Alkan, Dec 29 2015
STATUS
approved