A350992 Triangular numbers that are palindromes in base 7.

0, 1, 3, 6, 78, 171, 300, 2850, 8256, 9453, 14706, 120786, 208335, 399171, 405450, 416328, 448878, 720600, 5877306, 6046503, 6835753, 9350650, 10122750, 18431556, 19130205, 22596003, 35309406, 499169406, 934394835, 969430528, 999335571, 1059265378, 1730160900

Offset: 1

Author

Amiram Eldar, Jan 28 2022

Keywords

• nonn
• base

Comments

This sequence is infinite since A000217((7^k-1)/2) is a term for all k >= 0 (Trigg, 1974).

Examples

			78 is a term since 78 = A000217(12) is a triangular number and also a palindromic number in base 7: 78 = 141_7.
171 is a term since 171 = A000217(18) is a triangular number and also a palindromic number in base 7: 171 = 333_7.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..103
• Charles W. Trigg, Infinite sequences of palindromic triangular numbers, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212.

Crossrefs

Intersection of A000217 and A029954.

The septenary version of A003098.

Cf. A120741, A350987, A350990, A350991, A350993.

Programs

Mathematica

t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 7]] &]