Palindromic triangular numbers in base 2.
1, 11, 1111, 10101, 101101, 10011001, 11100111, 101000101, 1000110001, 1110000111, 100001100001, 111111111111, 10000011000001, 11100011000111, 1000000110000001, 1110001111000111, 1111100110011111, 11000110001100011, 100000001100000001
1
See S000344 for the n that produce these triangular numbers.
T. D. Noe, Plot of 109 terms
T. D. Noe, Table of 109 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]; t2 = ff[2, 40]; Table[FromDigits[IntegerDigits[n*(n + 1)/2, 2]], {n, t2}]
Cf. S000344.
nonn,base,hard
T. D. Noe, Nov 19 2014