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

1,3

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

Mathematica

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

Prog

(Haskell)
a213517 n = a213517_list !! (n-1)
a213517_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. A000217, A045914, A213516, A322570, A325907.

Cf. A118668.

Sequence in context: A154125 A106039 A151767 * A173899 A108897 A023767

Adjacent sequences: A213514 A213515 A213516 * A213518 A213519 A213520

Keyword

nonn,base

Author

T. D. Noe, Jun 21 2012

Status

approved