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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also n such that A001654(n)/(n+1) is an integer. LINKS Robert Price, Table of n, a(n) for n = 1..845 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 Cf. A000045, A001654, A007598. Sequence in context: A062371 A046030 A125726 * A244533 A180149 A155879 Adjacent sequences:  A175305 A175306 A175307 * A175309 A175310 A175311 KEYWORD easy,nonn AUTHOR Ctibor O. Zizka, Mar 26 2010 STATUS approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)