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

1,2

Comments

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000045, A001654, A101907, A140972.

Sequence in context: A028843 A028842 A260181 * A073689 A257560 A187774

Adjacent sequences: A140968 A140969 A140970 * A140972 A140973 A140974

Keyword

easy,nonn

Author

Ctibor O. Zizka, Jul 27 2008

Extensions

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

Status

approved