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Numbers n such that arithmetic mean of squares of the first n nonzero Fibonacci numbers is an integer.
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%I #7 May 02 2013 09:03:59

%S 1,2,3,5,7,12,13,15,17,23,24,25,36,37,43,47,48,50,53,60,67,72,73,75,

%T 83,96,97,103,107,108,110,113,120,125,127,137,144,157,163,167,168,170,

%U 173,175,180,192,193,195,197,216,223,227,233,240,257,263,277,283,288,293

%N Numbers n such that arithmetic mean of squares of the first n nonzero Fibonacci numbers is an integer.

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

%H Harvey P. Dale, <a href="/A140971/b140971.txt">Table of n, a(n) for n = 1..1000</a>

%F Numbers n such that A001654(n)/n is an integer.

%e n=2 : (A000045(1)^2+A000045(2)^2)/2 = 1

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

%Y Cf. A000045, A001654, A101907.

%K easy,nonn

%O 1,2

%A _Ctibor O. Zizka_, Jul 27 2008

%E Edited and extended by _R. J. Mathar_, Aug 05 2008