A213518 - OEIS

%I #20 Sep 21 2019 04:59:51

%S 4,5,6,7,8,9,12,13,18,24,34,44,58,66,77,100,101,105,109,114,132,141,

%T 363,666,714,816,1000,1095,1287,1332,1541,3363,6666,10000,10114,13332,

%U 66666,100000,133332,666666,1000000,1333332,6666666,10000000,13333332,33336636,66666666,100000000

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

%C 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.

%C A118668(a(n)) = 2. - _Reinhard Zumkeller_, Jul 11 2015

%C For n > 2, A325907(n) is a term. - _Seiichi Manyama_, Sep 15 2019

%H Seiichi Manyama and T. D. Noe <a href="/A213518/b213518.txt">Table of n, a(n) for n = 1..60</a> (first 51 terms from Seiichi Manyama)

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

%o (Haskell)

%o a213518 n = a213518_list !! (n-1)

%o a213518_list = filter ((== 2) . a118668) [0..]

%o -- _Reinhard Zumkeller_, Jul 11 2015

%o (PARI) for(k=0, 1e8, if(#Set(digits(k*(k+1)/2))==2, print1(k", "))) \\ _Seiichi Manyama_, Sep 15 2019

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

%Y Cf. A118668.

%Y Cf. A187127.

%K nonn,base

%O 1,1

%A _T. D. Noe_, Jun 22 2012

%E a(45)-a(48) from _Seiichi Manyama_, Sep 15 2019