Numbers n such that the n-th triangular number n*(n+1)/2 is a palindrome in base 6.
1, 2, 6, 7, 10, 41, 93, 98, 154, 259, 310, 628, 1406, 1540, 5698, 20237, 21266, 22867, 67081, 123170, 130289, 134923, 136147, 294678, 414982, 493210, 506797, 814276, 814516, 818275, 1928318, 2959333, 4882708, 5142040, 14482390, 17755930, 25512425, 26849585
1
Ulas makes no statement about base 6. See the base 6 numbers in S000356.
T. D. Noe, Plot of 46 terms
T. D. Noe, Table of 46 terms
Maciej Ulas, On certain diophantine equations related to triangular and tetrahedral numbers, arXiv 0811.2477 (Nov 15 2008)
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]; ff[6, 20]
Cf. A003098, A008509 (base 10), S000344-S000351 (bases 2-9) S000356.
nonn,base,hard
T. D. Noe, Nov 18 2014