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 A003098 M2605 #55 Mar 12 2025 10:37:51
%S A003098 0,1,3,6,55,66,171,595,666,3003,5995,8778,15051,66066,617716,828828,
%T A003098 1269621,1680861,3544453,5073705,5676765,6295926,35133153,61477416,
%U A003098 178727871,1264114621,1634004361,5289009825,6172882716,13953435931
%N A003098 Palindromic triangular numbers.
%C A003098 The only known terms with an even number 2*m of digits that are the concatenation of two palindromes with m digits are 55, 66 and 828828 (see David Wells entry 828828). - _Bernard Schott_, Apr 29 2022
%D A003098 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A003098 Charles W. Trigg, Palindromic Triangular Numbers, J. Rec. Math., 6 (1973), 146-147.
%D A003098 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 73 and p. 178, entry 828828 (Rev. ed. 1997)
%H A003098 T. D. Noe, <a href="/A003098/b003098.txt">Table of n, a(n) for n = 1..148</a> (from Patrick De Geest)
%H A003098 Patrick De Geest, <a href="http://www.worldofnumbers.com/triangle.htm">Palindromic Triangulars</a>
%H A003098 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_3">Triangular Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 83-125.
%t A003098 palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; Select[ Accumulate[ Range[200000]],palQ] (* _Harvey P. Dale_, Mar 23 2011 *)
%t A003098 Select[Accumulate[Range[0,170000]],PalindromeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 15 2019 *)
%o A003098 (PARI) list(lim)=my(v=List(),d); for(n=0,(sqrt(8*lim+1)-1)/2, d=digits(n*(n+1)/2); if(d==Vecrev(d), listput(v,n*(n+1)/2))); Vec(v) \\ _Charles R Greathouse IV_, Jun 23 2017
%o A003098 (Python)
%o A003098 A003098_list = [m for m in (n*(n+1)//2 for n in range(10**5)) if str(m) == str(m)[::-1]] # _Chai Wah Wu_, Sep 03 2021
%Y A003098 Cf. A008509.
%Y A003098 Intersection of A000217 and A002113.
%K A003098 nonn,base,nice
%O A003098 1,3
%A A003098 _N. J. A. Sloane_