%I #12 Jan 05 2025 19:51:42
%S 0,1,3,6,78,171,300,2850,8256,9453,14706,120786,208335,399171,405450,
%T 416328,448878,720600,5877306,6046503,6835753,9350650,10122750,
%U 18431556,19130205,22596003,35309406,499169406,934394835,969430528,999335571,1059265378,1730160900
%N Triangular numbers that are palindromes in base 7.
%C This sequence is infinite since A000217((7^k-1)/2) is a term for all k >= 0 (Trigg, 1974).
%H Amiram Eldar, <a href="/A350992/b350992.txt">Table of n, a(n) for n = 1..103</a>
%H Charles W. Trigg, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-2/trigg.pdf">Infinite sequences of palindromic triangular numbers</a>, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212.
%e 78 is a term since 78 = A000217(12) is a triangular number and also a palindromic number in base 7: 78 = 141_7.
%e 171 is a term since 171 = A000217(18) is a triangular number and also a palindromic number in base 7: 171 = 333_7.
%t t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 7]] &]
%Y Intersection of A000217 and A029954.
%Y The septenary version of A003098.
%Y Cf. A120741, A350987, A350990, A350991, A350993.
%K nonn,base
%O 1,3
%A _Amiram Eldar_, Jan 28 2022