cp's OEIS Frontend

A350990 Triangular numbers that are palindromes in base 3.

%I A350990 #15 Jan 05 2025 19:51:42
%S A350990 0,1,10,28,91,820,7381,65341,66430,597871,1633528,5380840,48339028,
%T A350990 48427561,139386556,435848050,1178284240,3529890253,3922632451,
%U A350990 32614707700,35296517971,35303692060,101891588176,292358957446,295883935480,317733228541,859413596320,2649105942220
%N A350990 Triangular numbers that are palindromes in base 3.
%C A350990 This sequence is infinite since A000217((3^k-1)/2) is a term for all k >= 0 (Trigg, 1971).
%H A350990 Amiram Eldar, <a href="/A350990/b350990.txt">Table of n, a(n) for n = 1..50</a>
%H A350990 Charles W. Trigg, <a href="https://doi.org/10.1111/j.1949-8594.1971.tb08858.x">Problem 3413</a>, Problem Department, School Science and Mathematics, Vol. 71, No. 9 (1971), p. 843; <a href="https://doi.org/10.1111/j.1949-8594.1972.tb08880.x">Solution to Problem 3413</a>, by Bob Prielipp, Vol. 72, No. 4 (1972), p. 358.
%H A350990 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 A350990 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 A350990 10 is a term since 10 = A000217(4) is a triangular number and also a palindromic number in base 3: 10 = 101_3.
%e A350990 28 is a term since 28 = A000217(7) is a triangular number and also a palindromic number in base 3: 36 = 1001_3.
%t A350990 t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 3]] &]
%Y A350990 Intersection of A000217 and A014190.
%Y A350990 The ternary version of A003098.
%Y A350990 Cf. A003462, A350987, A350991, A350992, A350993.
%K A350990 nonn,base
%O A350990 1,3
%A A350990 _Amiram Eldar_, Jan 28 2022