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 A140973 #20 Jul 04 2025 10:06:08
%S A140973 1,2,8,15,16,18,22,32,47,48,53,58,64,70,77,78,80,94,95,96,103,106,128,
%T A140973 138,163,199,206,256,257,266,269,311,326,330,352,358,385,397,398,401,
%U A140973 419,421,499,512,514,538,587,599,617,622,640,672,683,757,768,770,773
%N A140973 Numbers k such that arithmetic mean of squares of the first k tribonacci numbers is an integer.
%C A140973 Can the arithmetic mean of the tribonacci numbers (T(0)+...+T(k-1)) / k be an integer?
%C A140973 The arithmetic means are integers for the first 1, 2, 47, 53, 94, 103, 106, ... (A141579) tribonacci numbers. - _R. J. Mathar_, Aug 04 2008
%H A140973 Amiram Eldar, <a href="/A140973/b140973.txt">Table of n, a(n) for n = 1..10000</a>
%F A140973 Numbers k such that (T(0)^2+ T(1)^2+ ... + T(k-1)^2) / k is an integer, where T(i) = i-th tribonacci number.
%t A140973 With[{m = 1000}, Position[Accumulate[LinearRecurrence[{1, 1, 1}, {0, 0, 1}, m]^2] / Range[m], _?IntegerQ] // Flatten] (* _Amiram Eldar_, Jul 04 2025 *)
%Y A140973 Cf. A000073, A141579.
%Y A140973 Cf. A107239. - _R. J. Mathar_, Aug 04 2008
%K A140973 easy,nonn
%O A140973 1,2
%A A140973 _Ctibor O. Zizka_, Jul 27 2008
%E A140973 a(1)-a(2) inserted and a(32) onwards added by _R. J. Mathar_, Aug 04 2008