A140971 Numbers k such that arithmetic mean of squares of the first k nonzero Fibonacci numbers is an integer.

1, 2, 3, 5, 7, 12, 13, 15, 17, 23, 24, 25, 36, 37, 43, 47, 48, 50, 53, 60, 67, 72, 73, 75, 83, 96, 97, 103, 107, 108, 110, 113, 120, 125, 127, 137, 144, 157, 163, 167, 168, 170, 173, 175, 180, 192, 193, 195, 197, 216, 223, 227, 233, 240, 257, 263, 277, 283, 288, 293

Offset: 1

Author

Ctibor O. Zizka, Jul 27 2008

Keywords

• easy
• nonn

Comments

Is the root mean square RMS(F(0),...,F(k-1)) an integer for some k?

Examples

			k = 2: (A000045(1)^2+A000045(2)^2)/2 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000045, A001654, A101907, A140972.

Programs

Mathematica

nn=300;With[{fib2=Fibonacci[Range[nn]]^2},Flatten[Position[Table[ Mean[ Take[ fib2,n]],{n,nn}],?IntegerQ]]] (* _Harvey P. Dale, May 02 2013 *)

Formula

Numbers k such that A001654(k)/k is an integer.

Extensions

Edited and extended by R. J. Mathar, Aug 05 2008