A350990 Triangular numbers that are palindromes in base 3.

0, 1, 10, 28, 91, 820, 7381, 65341, 66430, 597871, 1633528, 5380840, 48339028, 48427561, 139386556, 435848050, 1178284240, 3529890253, 3922632451, 32614707700, 35296517971, 35303692060, 101891588176, 292358957446, 295883935480, 317733228541, 859413596320, 2649105942220

Offset: 1

Author

Amiram Eldar, Jan 28 2022

Keywords

• nonn
• base

Comments

This sequence is infinite since A000217((3^k-1)/2) is a term for all k >= 0 (Trigg, 1971).

Examples

			10 is a term since 10 = A000217(4) is a triangular number and also a palindromic number in base 3: 10 = 101_3.
28 is a term since 28 = A000217(7) is a triangular number and also a palindromic number in base 3: 36 = 1001_3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..50
• Charles W. Trigg, Problem 3413, Problem Department, School Science and Mathematics, Vol. 71, No. 9 (1971), p. 843; Solution to Problem 3413, by Bob Prielipp, Vol. 72, No. 4 (1972), p. 358.
• Charles W. Trigg, Infinite sequences of palindromic triangular numbers, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212.
• Maciej Ulas, On certain diophantine equations related to triangular and tetrahedral numbers, arXiv:0811.2477 [math.NT], 2008.

Crossrefs

Intersection of A000217 and A014190.

The ternary version of A003098.

Cf. A003462, A350987, A350991, A350992, A350993.

Programs

Mathematica

t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 3]] &]