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A175308
Numbers n such that (Sum_{i=0..n} F(i)^2) / (n+1) is an integer, where F(i) i-th Fibonacci number.
1
0, 4, 9, 10, 11, 18, 23, 24, 28, 30, 35, 40, 47, 58, 59, 60, 70, 71, 78, 88, 95, 100, 104, 107, 108, 119, 124, 130, 138, 143, 148, 150, 167, 178, 179, 180, 190, 191, 198, 210, 215, 228, 238, 239, 240, 249, 250, 268, 270, 272, 280, 287, 299, 310, 323, 330, 335
OFFSET
1,2
COMMENTS
Also n such that A001654(n)/(n+1) is an integer.
LINKS
EXAMPLE
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.
MATHEMATICA
lst = {}; sm = 0; Do[sm = sm + Fibonacci[n]^2; If[Mod[sm, n + 1] == 0, AppendTo[lst, n]], {n, 0, 335}]; lst
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Mar 26 2010
STATUS
approved