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

1,3

Comments

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

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.

Example

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.

Mathematica

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

Crossrefs

Intersection of A000217 and A029954.

The septenary version of A003098.

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

Sequence in context: A282175 A182966 A023174 * A213138 A364798 A349875

Adjacent sequences: A350989 A350990 A350991 * A350993 A350994 A350995

Keyword

nonn,base

Author

Amiram Eldar, Jan 28 2022

Status

approved