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

1,1

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).

Mathematica

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

Prog

(Haskell)
a213518 n = a213518_list !! (n-1)
a213518_list = filter ((== 2) . a118668) [0..]
-- Reinhard Zumkeller, Jul 11 2015
(PARI) for(k=0, 1e8, if(#Set(digits(k*(k+1)/2))==2, print1(k", "))) \\ Seiichi Manyama, Sep 15 2019

Crossrefs

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

Cf. A118668.

Cf. A187127.

Sequence in context: A321353 A161674 A285623 * A214419 A189481 A123977

Adjacent sequences: A213515 A213516 A213517 * A213519 A213520 A213521

Keyword

nonn,base

Author

T. D. Noe, Jun 22 2012

Extensions

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

Status

approved