S000346


Numbers n such that the n-th triangular number n*(n+1)/2 is a palindrome in base 4.

1, 2, 4, 5, 6, 10, 14, 19, 25, 35, 36, 90, 102, 330, 1389, 1445, 1702, 2666, 5985, 8523, 8700, 10146, 22629, 23425, 32489, 35427, 41277, 53625, 58990, 79155, 183237, 294020, 463409, 711533, 945550, 1280915, 7116473, 9141699, 14653745, 22855474, 37958779

1

S000346

Ulas makes no statement about base 4. See the base 4 numbers in S000354.

T. D. Noe, Plot of 47 terms

T. D. Noe, Table of 47 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[4, 20]

Cf. A003098A008509 (base 10), S000344-S000351 (bases 2-9), S000354.

nonn,base,hard

T. D. Noe, Nov 18 2014

© Tony D Noe 2014-2015