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 A101907 Numbers n-1 such that the arithmetic mean of the first n Fibonacci numbers (beginning with F(0)) is an integer. 6
 0, 3, 5, 8, 10, 18, 23, 28, 30, 33, 40, 45, 47, 58, 60, 70, 71, 78, 88, 93, 95, 99, 100, 105, 108, 119, 128, 130, 138, 143, 148, 150, 165, 178, 180, 190, 191, 198, 200, 210, 213, 215, 219, 225, 228, 238, 239, 240, 248, 250, 268, 270, 273, 280, 287, 310, 320, 330 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sum of the first n Fibonacci numbers is F(n+2)-1, sequence A000071. Knott discusses the factorization of these numbers. - T. D. Noe, Oct 10 2005 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. [From Ctibor O. Zizka, Aug 06 2008] M. Ward, The prime divisors of Fibonacci numbers, Pacific J. Math., Vol. 11, No. 1 (1961), pp. 379-386. [From Ctibor O. Zizka, Aug 06 2008] 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 Cf. A000045, A000071. See A111035 for another version. Cf. A219612. - Altug Alkan, Dec 29 2015 Sequence in context: A212987 A217919 A127700 * A242250 A117668 A184410 Adjacent sequences:  A101904 A101905 A101906 * A101908 A101909 A101910 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

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Last modified July 11 08:53 EDT 2020. Contains 335626 sequences. (Running on oeis4.)