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 A008509 #25 Aug 11 2024 14:41:29
%S A008509 1,2,3,10,11,18,34,36,77,109,132,173,363,1111,1287,1593,1833,2662,
%T A008509 3185,3369,3548,8382,11088,18906,50281,57166,102849,111111,167053,
%U A008509 179158,246642,337650,342270,365436,417972,1620621,3240425,3457634,3707883
%N A008509 Positive integers k such that k-th triangular number is palindromic.
%D A008509 Charles W. Trigg, Palindromic Triangular Numbers, J. Rec. Math., 6 (1973), 146-147.
%D A008509 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 93.
%H A008509 T. D. Noe, <a href="/A008509/b008509.txt">Table of n, a(n) for n = 1..147</a> (from P. De Geest)
%H A008509 P. De Geest, <a href="https://www.worldofnumbers.com/triangle.htm">Palindromic Triangulars</a>
%t A008509 palQ[n_]:= Reverse[x=IntegerDigits[n]]==x; t={}; Do[If[palQ[n*(n+1)/2],AppendTo[t,n]],{n,4*10^6}]; t (* _Jayanta Basu_, May 13 2013 *)
%t A008509 Position[Accumulate[Range[371*10^4]],_?PalindromeQ]//Flatten (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 12 2020 *)
%o A008509 (PARI) ispal(n)=n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1
%o A008509 is(n)=ispal(n*(n+1)/2) \\ _Charles R Greathouse IV_, May 15 2013
%o A008509 (Magma) [k:k in [1..5000000]| Intseq(Binomial(k+1,2)) eq Reverse(Intseq(Binomial(k+1,2)))]; // _Marius A. Burtea_, Jul 16 2019
%Y A008509 Cf. A003098, A002113, A000217, A083571, A050721, A050722.
%K A008509 nonn,base
%O A008509 1,2
%A A008509 _Patrick De Geest_