Numbers n such that the n-th triangular number n*(n+1)/2 is a palindrome in base 5.
1, 2, 3, 8, 12, 27, 62, 203, 216, 312, 543, 692, 923, 948, 1562, 2076, 3467, 5408, 7812, 12183, 12191, 17267, 25071, 26516, 39062, 125678, 135216, 142838, 195312, 268151, 276471, 591551, 616528, 976562, 1592088, 1612863, 2886576, 2891576, 3524688, 3658236
1
Ulas proves that this sequence is infinite. See the base 5 numbers in S000355.
T. D. Noe, Plot of 52 terms
T. D. Noe, Table of 52 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[5, 20]
Cf. A003098, A008509 (base 10), S000344-S000351 (bases 2-9), S000355.
nonn,base,hard
T. D. Noe, Nov 18 2014