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

%I A213517 #24 Sep 15 2019 10:50:43
%S A213517 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,
%T A213517 109,114,132,141,363,666,714,816,1000,1095,1287,1332,1541,3363,6666,
%U A213517 10000,10114,13332,66666,100000,133332,666666,1000000,1333332,6666666,10000000
%N A213517 Numbers n such that the triangular number n*(n+1)/2 has only 1 or 2 different digits in base 10.
%C A213517 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 A213517 A118668(a(n)) <= 2. - _Reinhard Zumkeller_, Jul 11 2015
%C A213517 A325907(n) is a term. - _Seiichi Manyama_, Sep 14 2019
%H A213517 Seiichi Manyama, <a href="/A213517/b213517.txt">Table of n, a(n) for n = 1..58</a>
%t A213517 t = {}; Do[tri = n*(n+1)/2; If[Length[Union[IntegerDigits[tri]]] <= 2, AppendTo[t, n]], {n, 0, 10^5}]; t
%o A213517 (Haskell)
%o A213517 a213517 n = a213517_list !! (n-1)
%o A213517 a213517_list = filter ((<= 2) . a118668) [0..]
%o A213517 -- _Reinhard Zumkeller_, Jul 11 2015
%o A213517 (PARI) for(k=0, 1e8, if(#Set(digits(k*(k+1)/2))<=2, print1(k", "))) \\ _Seiichi Manyama_, Sep 15 2019
%Y A213517 Cf. A000217, A045914, A213516, A322570, A325907.
%Y A213517 Cf. A118668.
%K A213517 nonn,base
%O A213517 1,3
%A A213517 _T. D. Noe_, Jun 21 2012