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

1,1

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

Links

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

Example

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

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

Prog

(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

Crossrefs

Cf. A000217.

Subsequence of A020756.

Sequence in context: A118878 A036208 A119903 * A127994 A025391 A025382

Adjacent sequences: A113793 A113794 A113795 * A113797 A113798 A113799

Keyword

nonn,base

Author

Giovanni Resta, Jan 21 2006

Extensions

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

Status

approved