A350991 Triangular numbers that are palindromes in base 5.

0, 1, 3, 6, 36, 78, 378, 1953, 20706, 23436, 48828, 147696, 239778, 426426, 449826, 1220703, 2155926, 6011778, 14625936, 30517578, 74218836, 74316336, 149083278, 314290056, 351562386, 762939453, 7897542681, 9141750936, 10201418541, 19073486328, 35952613476, 38218245156

Offset: 1

Author

Amiram Eldar, Jan 28 2022

Keywords

• nonn
• base

Comments

This sequence is infinite since A000217((5^k-1)/2) is a term for all k >= 0 (Trigg, 1972).

Examples

			6 is a term since 6 = A000217(3) is a triangular number and also a palindromic number in base 5: 6 = 11_5.
36 is a term since 36 = A000217(8) is a triangular number and also a palindromic number in base 5: 36 = 121_5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..68
• Charles W. Trigg, Problem 840, Problems and Solutions, Mathematics Magazine, Vol. 45, No. 4 (1972), p. 228; Triangular Palindromes, Solution to Problem 840 by E. P. Starke, ibid., Vol. 46, No. 3 (1973), p. 170.
• 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 A029952.

The quinary version of A003098.

Cf. A003098, A125831, A350987, A350990, A350992, A350993.

Programs

Mathematica

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