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%I #10 May 05 2013 14:57:36
%S 0,4,9,10,11,18,23,24,28,30,35,40,47,58,59,60,70,71,78,88,95,100,104,
%T 107,108,119,124,130,138,143,148,150,167,178,179,180,190,191,198,210,
%U 215,228,238,239,240,249,250,268,270,272,280,287,299,310,323,330,335
%N Numbers n such that (Sum_{i=0..n} F(i)^2) / (n+1) is an integer, where F(i) i-th Fibonacci number.
%C Also n such that A001654(n)/(n+1) is an integer.
%H Robert Price, <a href="/A175308/b175308.txt">Table of n, a(n) for n = 1..845</a>
%e For n=0 we have : 0*0/1=0 so n=0 belongs to the sequence. For n=4 we have : (0*0+1*1+1*1+2*2+3*3)/5=3 so n=5 belongs to the sequence. For n=9 we have : (0*0+1*1+1*1+2*2+3*3+5*5+8*8+13*13+21*21+34*34)/10=187 so n=9 belongs to the sequence.
%t lst = {}; sm = 0; Do[sm = sm + Fibonacci[n]^2; If[Mod[sm, n + 1] == 0, AppendTo[lst, n]], {n, 0, 335}]; lst
%Y Cf. A000045, A001654, A007598.
%K easy,nonn
%O 1,2
%A _Ctibor O. Zizka_, Mar 26 2010