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

1,3

Comments

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

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.

Example

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.

Mathematica

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

Crossrefs

Intersection of A000217 and A029952.

The quinary version of A003098.

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

Sequence in context: A119198 A119196 A119184 * A084260 A076983 A068084

Adjacent sequences: A350988 A350989 A350990 * A350992 A350993 A350994

Keyword

nonn,base

Author

Amiram Eldar, Jan 28 2022

Status

approved