A213516 Triangular numbers having only 1 or 2 different digits in base 10.

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 171, 300, 595, 666, 990, 1711, 2211, 3003, 5050, 5151, 5565, 5995, 6555, 8778, 10011, 66066, 222111, 255255, 333336, 500500, 600060, 828828, 887778, 1188111, 5656566, 22221111, 50005000, 51151555, 88877778

Offset: 1

Author

T. D. Noe, Jun 21 2012

Keywords

• nonn
• base

Comments

The list of triangular numbers containing only one digit (A045914) is finite. This list is infinite because numbers like 8888777778, 222222111111, and 500000500000 occur an infinite number of times.

A309597 is a subsequence. - Seiichi Manyama, Sep 14 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A000217, A045914, A213517, A309597, A319170.

Cf. A119033 (has list of sequences related to digits in triangular numbers).

Programs

Magma

[n*(n+1)/2: n in [0..10^5] | #Set(Intseq(n*(n+1) div 2)) le 2]; // Bruno Berselli, Oct 27 2012

Mathematica

t = {}; Do[tri = n*(n+1)/2; If[Length[Union[IntegerDigits[tri]]] <= 2, AppendTo[t, tri]], {n, 0, 10^5}]; t
Select[Accumulate[Range[0,20000]],Count[DigitCount[#],0]>7&] (* Harvey P. Dale, Sep 03 2020 *)