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 A185223 #25 Dec 28 2024 21:57:02
%S A185223 6,18,37,44,86,91,116,132,247,278,392,613,637,662,798,847,912,1164,
%T A185223 1235,1362,1430,1638,1735,1991,2056,2090,2167,2364,2537,2736,3139,
%U A185223 3478,3751,3867,4298,4422,4553,5202,6068,6391,6500,7241,7859,7957,8378,9309,9793
%N A185223 A185128(n) is the a(n)-th triangular number.
%C A185223 Side lengths where both triangular numbers are the same (A053141) are not included. - _R. J. Mathar_, Feb 11 2018
%C A185223 See A185128 for further information.
%D A185223 Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, no. 8.
%H A185223 R. J. Mathar, <a href="/A185223/b185223.txt">Table of n, a(n) for n = 1..58</a>
%H A185223 N. J. A. Sloane, <a href="/A185128/a185128.jpg">Annotated scan of Beiler's Table 81</a>, based on page 197 of Beiler's "Recreations in the Theory of Numbers: The Queen of Mathematics Entertains", New York, Dover, First ed., 1964.
%e A185223 A185128(2) = 171 which is the 18th triangular number, so a(2) = 18.
%o A185223 (PARI) lista(nn) = {v = vector(nn, n, n*(n+1)/2); for (n=2, nn, for (k=1, n-1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]-v[k], 3), print1(n, ", "));););} \\ _Michel Marcus_, Jan 08 2015
%Y A185223 Cf. A000217, A185128, A185129, A185233, A185243, A185253, A185257, A185258.
%K A185223 nonn
%O A185223 1,1
%A A185223 _Martin Renner_, Jan 20 2012
%E A185223 Edited (with a simpler definition) by _N. J. A. Sloane_, Dec 28 2024