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 A350993 #21 Jan 05 2025 19:51:42 %S A350993 0,1,3,6,10,91,136,300,528,820,4560,7381,11476,20910,42486,66430, %T A350993 552826,581581,597871,1664400,2001000,3420420,3444000,5070520,5380840, %U A350993 48427561,75995956,132494781,134553810,137158203,159213090,290585778,434520460,435848050,669615310 %N A350993 Triangular numbers that are palindromes in base 9. %C A350993 This sequence is infinite since A000217((9^k-1)/2) is a term for all k >= 0 (Wishard, 1931). %C A350993 Also, A000217((3 + 5*9^k)/2) is a term for all k>=0 (Trigg, 1984). %D A350993 Charles W. Trigg, Mathematical Quickies, McGraw Hill Book Co., 1967, Q112, p. 127. %H A350993 Amiram Eldar, <a href="/A350993/b350993.txt">Table of n, a(n) for n = 1..123</a> %H A350993 Charles W. Trigg, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-2/trigg.pdf">Infinite sequences of palindromic triangular numbers</a>, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212. %H A350993 Charles W. Trigg, <a href="https://www.jstor.org/stable/2686405">Problem 281</a>, The College Mathematics Journal, Vol. 15, No. 4 (1984), p. 346; <a href="http://www.jstor.org/stable/2686843">Palindromic Triangular Numbers in Base Nine</a>, Solution to Problem 281, by Michael Vowe, ibid., Vol. 17, No. 2 (1986), pp. 188-189. %H A350993 Maciej Ulas, <a href="https://arxiv.org/abs/0811.2477">On certain diophantine equations related to triangular and tetrahedral numbers</a>, arXiv:0811.2477 [math.NT], 2008. %H A350993 G. W. Wishard, <a href="https://www.jstor.org/stable/2300979">Problem 3480</a>, The American Mathematical Monthly, Vol. 38, No. 3 (1931), p. 170; <a href="https://www.jstor.org/stable/2302299">Solution to Problem 3480</a>, by Helen A. Merrill, ibid., Vol. 39, No. 3 (1932), p. 179. %e A350993 10 is a term since 10 = A000217(4) is a triangular number and also a palindromic number in base 9: 10 = 11_9. %e A350993 91 is a term since 91 = A000217(13) is a triangular number and also a palindromic number in base 9: 91 = 111_9. %t A350993 t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 9]] &] %Y A350993 Intersection of A000217 and A029955. %Y A350993 The nonary version of A003098. %Y A350993 Cf. A191681, A350987, A350990, A350991, A350992. %K A350993 nonn,base %O A350993 1,3 %A A350993 _Amiram Eldar_, Jan 28 2022