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.

190, 191, 19900, 19901, 90415, 585910, 1201545, 1414910, 1501726, 1909415, 1999000, 1999001, 2442196, 7003676, 7693846, 14745226, 28296970, 30307171, 42009156, 47748526, 61549231, 63249300, 78049756, 82749850, 84559880, 115449880, 117259850, 121959756

Offset: 1

Author

Giovanni Resta, Jan 21 2006

Keywords

• nonn
• base

Comments

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

Examples

			90415 = T(90) + T(415).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..56 (first 41 terms from Michael S. Branicky)

Crossrefs

Cf. A000217.

Subsequence of A020756.

Programs

Mathematica

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

Python

def T(n): return n*(n+1)//2
def ok(n):
    if n < 10: return False
    s = str(n)
    splits = ((int(s[:i]), int(s[i:])) for i in range(1, len(s)))
    return any(n == T(x) + T(y) for x, y in splits)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jan 22 2022

Extensions

a(26)-a(28) from Michael S. Branicky, Jan 22 2022