A213517 Numbers n such that the triangular number n*(n+1)/2 has only 1 or 2 different digits in base 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 24, 34, 36, 44, 58, 66, 77, 100, 101, 105, 109, 114, 132, 141, 363, 666, 714, 816, 1000, 1095, 1287, 1332, 1541, 3363, 6666, 10000, 10114, 13332, 66666, 100000, 133332, 666666, 1000000, 1333332, 6666666, 10000000

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 133332, 666666, and 1000000 occur an infinite number of times.

A118668(a(n)) <= 2. - Reinhard Zumkeller, Jul 11 2015

A325907(n) is a term. - Seiichi Manyama, Sep 14 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..58

Crossrefs

Cf. A000217, A045914, A213516, A322570, A325907.

Cf. A118668.

Programs

Haskell

a213517 n = a213517_list !! (n-1)
a213517_list = filter ((<= 2) . a118668) [0..]
-- Reinhard Zumkeller, Jul 11 2015

Mathematica

t = {}; Do[tri = n*(n+1)/2; If[Length[Union[IntegerDigits[tri]]] <= 2, AppendTo[t, n]], {n, 0, 10^5}]; t

PARI

for(k=0, 1e8, if(#Set(digits(k*(k+1)/2))<=2, print1(k", "))) \\ Seiichi Manyama, Sep 15 2019