This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140971 #16 Jul 04 2025 10:05:15
%S A140971 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 A140971 83,96,97,103,107,108,110,113,120,125,127,137,144,157,163,167,168,170,
%U A140971 173,175,180,192,193,195,197,216,223,227,233,240,257,263,277,283,288,293
%N A140971 Numbers k such that arithmetic mean of squares of the first k nonzero Fibonacci numbers is an integer.
%C A140971 Is the root mean square RMS(F(0),...,F(k-1)) an integer for some k?
%H A140971 Amiram Eldar, <a href="/A140971/b140971.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F A140971 Numbers k such that A001654(k)/k is an integer.
%e A140971 k = 2: (A000045(1)^2+A000045(2)^2)/2 = 1.
%t A140971 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 A140971 Cf. A000045, A001654, A101907, A140972.
%K A140971 easy,nonn
%O A140971 1,2
%A A140971 _Ctibor O. Zizka_, Jul 27 2008
%E A140971 Edited and extended by _R. J. Mathar_, Aug 05 2008