A175308 Numbers n such that (Sum_{i=0..n} F(i)^2) / (n+1) is an integer, where F(i) i-th Fibonacci number.

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

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: A046030 A125726 A352323 * A244533 A180149 A155879

Adjacent sequences: A175305 A175306 A175307 * A175309 A175310 A175311

Keyword

easy,nonn

Author

Ctibor O. Zizka, Mar 26 2010

Status

approved