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%I #14 Jan 18 2024 09:58:18
%S 0,1,3,6,36,78,378,1953,20706,23436,48828,147696,239778,426426,449826,
%T 1220703,2155926,6011778,14625936,30517578,74218836,74316336,
%U 149083278,314290056,351562386,762939453,7897542681,9141750936,10201418541,19073486328,35952613476,38218245156
%N Triangular numbers that are palindromes in base 5.
%C This sequence is infinite since A000217((5^k-1)/2) is a term for all k >= 0 (Trigg, 1972).
%H Amiram Eldar, <a href="/A350991/b350991.txt">Table of n, a(n) for n = 1..68</a>
%H Charles W. Trigg, <a href="https://www.jstor.org/stable/2688667">Problem 840</a>, Problems and Solutions, Mathematics Magazine, Vol. 45, No. 4 (1972), p. 228; <a href="https://www.jstor.org/stable/2687977">Triangular Palindromes</a>, Solution to Problem 840 by E. P. Starke, ibid., Vol. 46, No. 3 (1973), p. 170.
%H Charles W. Trigg, <a href="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 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.
%e 6 is a term since 6 = A000217(3) is a triangular number and also a palindromic number in base 5: 6 = 11_5.
%e 36 is a term since 36 = A000217(8) is a triangular number and also a palindromic number in base 5: 36 = 121_5.
%t t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 5]] &]
%Y Intersection of A000217 and A029952.
%Y The quinary version of A003098.
%Y Cf. A003098, A125831, A350987, A350990, A350992, A350993.
%K nonn,base
%O 1,3
%A _Amiram Eldar_, Jan 28 2022
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