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

%I A213518 #27 Aug 25 2025 11:41:41
%S A213518 4,5,6,7,8,9,12,13,18,24,34,44,58,66,77,100,101,105,109,114,132,141,
%T A213518 363,666,714,816,1000,1095,1287,1332,1541,3363,6666,10000,10114,13332,
%U A213518 66666,100000,133332,666666,1000000,1333332,6666666,10000000,13333332,33336636,66666666,100000000
%N A213518 Numbers k such that the triangular number k*(k+1)/2 has 2 different digits in base 10.
%C A213518 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 A213518 A118668(a(n)) = 2. - _Reinhard Zumkeller_, Jul 11 2015
%C A213518 For n > 2, A325907(n) is a term. - _Seiichi Manyama_, Sep 15 2019
%H A213518 David Radcliffe, <a href="/A213518/b213518.txt">Table of n, a(n) for n = 1..116</a> (terms 1..51 from Seiichi Manyama, terms 52..60 from T. D. Noe).
%t A213518 t = {}; Do[tri = n*(n+1)/2; If[Length[Union[IntegerDigits[tri]]] == 2, AppendTo[t, n]], {n, 10^5}]; t
%o A213518 (Haskell)
%o A213518 a213518 n = a213518_list !! (n-1)
%o A213518 a213518_list = filter ((== 2) . a118668) [0..]
%o A213518 -- _Reinhard Zumkeller_, Jul 11 2015
%o A213518 (PARI) for(k=0, 1e8, if(#Set(digits(k*(k+1)/2))==2, print1(k", "))) \\ _Seiichi Manyama_, Sep 15 2019
%Y A213518 Cf. A062691 (the corresponding triangular numbers), A213516, A213517, A325907.
%Y A213518 Cf. A118668.
%Y A213518 Cf. A187127.
%K A213518 nonn,base,changed
%O A213518 1,1
%A A213518 _T. D. Noe_, Jun 22 2012
%E A213518 a(45)-a(48) from _Seiichi Manyama_, Sep 15 2019