A213518 Numbers k such that the triangular number k*(k+1)/2 has 2 different digits in base 10.

4, 5, 6, 7, 8, 9, 12, 13, 18, 24, 34, 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, 13333332, 33336636, 66666666, 100000000

Offset: 1

Author

T. D. Noe, Jun 22 2012

Keywords

• nonn
• base
• changed

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

For n > 2, A325907(n) is a term. - Seiichi Manyama, Sep 15 2019

Links

• David Radcliffe, Table of n, a(n) for n = 1..116 (terms 1..51 from Seiichi Manyama, terms 52..60 from T. D. Noe).

Crossrefs

Cf. A062691 (the corresponding triangular numbers), A213516, A213517, A325907.

Cf. A118668.

Cf. A187127.

Programs

Haskell

a213518 n = a213518_list !! (n-1)
a213518_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, 10^5}]; t

PARI

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

Extensions

a(45)-a(48) from Seiichi Manyama, Sep 15 2019