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 A140972 #15 Jul 05 2025 11:25:26
%S A140972 1,10,12,24,36,48,60,72,96,108,120,144,168,180,192,216,240,250,288,
%T A140972 300,324,336,360,384,432,442,480,504,540,550,552,576,600,612,624,648,
%U A140972 660,672,684,720,768,840,864,900,960,972,1008,1068,1080,1104,1152,1176,1200
%N A140972 Numbers k such that arithmetic mean of squares of first k Lucas numbers is an integer.
%C A140972 The root mean square RMS(L(0),...,L(k-1)) is firstly an integer for k = 36.
%H A140972 Amiram Eldar, <a href="/A140972/b140972.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F A140972 k such that (L(0)^2+ L(1)^2+ ... + L(k-1)^2) / k is an integer, where L(i) is the i-th Lucas number.
%e A140972 k = 10: (L(0)^2+...+L(9)^2)/10 = 935.
%t A140972 With[{nn=1200},Transpose[Select[Thread[{Range[nn],Accumulate[ LucasL[ Range[0,nn-1]]^2]}],IntegerQ[Last[#]/First[#]]&]][[1]]] (* _Harvey P. Dale_, Jul 15 2012 *)
%o A140972 (PARI) list(lim) = {my(L1 = 2, L2 = 1, s = 5); print1(1, ", "); for(k = 3, lim, L3 = L1 + L2; s += L3^2; if(!(s % k), print1(k, ", ")); L1 = L2; L2 = L3);} \\ _Amiram Eldar_, Jul 04 2025
%Y A140972 Cf. A000032, A140480, A140971.
%K A140972 easy,nonn
%O A140972 1,2
%A A140972 _Ctibor O. Zizka_, Jul 27 2008
%E A140972 a(1) inserted and a(48) onwards added by _R. J. Mathar_, Aug 04 2008