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A113796 Numbers k such that k = T(x) + T(y) where T(m) is the m-th triangular number and k is concatenate(x, y) in base 10.

%I A113796 #28 Jan 22 2022 19:13:09
%S A113796 190,191,19900,19901,90415,585910,1201545,1414910,1501726,1909415,
%T A113796 1999000,1999001,2442196,7003676,7693846,14745226,28296970,30307171,
%U A113796 42009156,47748526,61549231,63249300,78049756,82749850,84559880,115449880,117259850,121959756
%N A113796 Numbers k such that k = T(x) + T(y) where T(m) is the m-th triangular number and k is concatenate(x, y) in base 10.
%C A113796 Contains (2*10^i - 1)*10^i and (2*10^i - 1)*10^i + 1 for all i >= 1. - _Michael S. Branicky_, Jan 22 2022
%H A113796 David A. Corneth, <a href="/A113796/b113796.txt">Table of n, a(n) for n = 1..56</a> (first 41 terms from Michael S. Branicky)
%e A113796 90415 = T(90) + T(415).
%t A113796 lst = {}; t[n_] := n(n + 1)/2; Do[p=10; While[n > p, If[t[Mod[n, p]] + t[Floor[n/p]] == n, AppendTo[lst, n]]; p*= 10], {n, 10^6}]; lst
%o A113796 (Python)
%o A113796 def T(n): return n*(n+1)//2
%o A113796 def ok(n):
%o A113796     if n < 10: return False
%o A113796     s = str(n)
%o A113796     splits = ((int(s[:i]), int(s[i:])) for i in range(1, len(s)))
%o A113796     return any(n == T(x) + T(y) for x, y in splits)
%o A113796 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Jan 22 2022
%Y A113796 Cf. A000217.
%Y A113796 Subsequence of A020756.
%K A113796 nonn,base
%O A113796 1,1
%A A113796 _Giovanni Resta_, Jan 21 2006
%E A113796 a(26)-a(28) from _Michael S. Branicky_, Jan 22 2022