Palindromic triangular numbers in base 3.
1, 101, 1001, 10101, 1010101, 101010101, 10022122001, 10101010101, 1010101010101, 10001222210001, 101010101010101, 10100221212200101, 10101010101010101, 100201021120102001, 1010101010101010101, 10001010011001010001, 100010000010000010001
1
See S000345 for the n that produce these triangular numbers.
T. D. Noe, Plot of 38 terms
T. D. Noe, Table of 38 terms
Eric W. Weisstein, MathWorld: Triangular Number
(Mma) ff[base_, len_] := Module[{n = 0, t = {}, tri, d}, While[Length[t] < len, n++; tri = n*(n + 1)/2; d = IntegerDigits[tri, base]; If[d == Reverse[d], AppendTo[t, n]]]; t]; t3 = ff[3, 20]; Table[FromDigits[IntegerDigits[n*(n + 1)/2, 3]], {n, t3}]
Cf. S000345.
nonn,base,hard
T. D. Noe, Nov 19 2014