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

1,3

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

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 *)

Prog

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

Crossrefs

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

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

Sequence in context: A069695 A069697 A069699 * A078254 A069700 A069698

Adjacent sequences: A213513 A213514 A213515 * A213517 A213518 A213519

Keyword

nonn,base

Author

T. D. Noe, Jun 21 2012

Status

approved