A213518 -id:A213518 - cp's OEIS frontend

A062691 Triangular numbers that contain exactly 2 different digits.

10, 15, 21, 28, 36, 45, 78, 91, 171, 300, 595, 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, 2222211111, 5000050000

Offset: 1

Erich Friedman, Jul 04 2001

For n > 2, A309597(n) is a term. - Seiichi Manyama, Sep 15 2019

The other known infinite families of terms are A037156(n) for n > 1, A319170(n), and A383942(n). - David Radcliffe, Aug 25 2025

			300 is triangular and contains the digits 0 and 3.

David Radcliffe, Table of n, a(n) for n = 1..116 (terms 1..51 from Seiichi Manyama).

Cf. A000217, A045914 (all digits the same), A213516, A213518, A309597.

Select[Accumulate[Range[14000]],Count[DigitCount[#],Except[0]]==2&] (* Harvey P. Dale, Nov 27 2011 *)

for(k=0, 1e5, if(#Set(digits(j=k*(k+1)/2))==2, print1(j", "))) \\ Seiichi Manyama, Sep 15 2019

A118668 Number of distinct digits needed to write the n-th triangular number in decimal representation.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 1, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 2, 3, 4, 3, 4, 4, 3, 4, 2, 3, 4, 4, 4, 3, 3, 4, 3, 4, 3, 2, 4, 4, 4, 3, 3, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 2, 2, 3, 3, 4

Offset: 0

Reinhard Zumkeller, May 19 2006

0 < a(n) <= 10;

a(n) = A043537(A000217(n)).

			n=99: 99*(99+1)/2 = 4950 -> a(99) = #{0,4,5,9} = 4;
see A119033 for an overview of sequences with terms composed of not more than 3 distinct digits.
n=100: 100*(100+1)/2 = 5050 -> a(100) = #{0,5} = 2;

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A000217, A043537, A045914, A213517, A213518, A255678.

a118668 = a043537 . a000217
a118668_list = map a043537 a000217_list
-- Reinhard Zumkeller, Jul 11 2015

Length[Union[IntegerDigits[#]]]&/@Accumulate[Range[0,110]] (* Harvey P. Dale, Jul 23 2012 *)

cp's OEIS Frontend

A062691 Triangular numbers that contain exactly 2 different digits.

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