A102766 Numbers n that can be chopped into two parts, which when added and squared result in n.

1, 81, 100, 2025, 3025, 9801, 10000, 88209, 494209, 998001, 1000000, 4941729, 7441984, 23804641, 24502500, 25502500, 28005264, 52881984, 60481729, 99980001, 100000000, 300814336, 493817284, 1518037444, 6049417284, 6832014336, 9048004641, 9999800001, 10000000000

Offset: 1

Author

Bodo Zinser, Feb 10 2005

Keywords

• nonn
• base

Examples

			a(7) = 88209 is a term as (88+209)^2 = 297^2 = 88209.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..131
• Henry Ernest Dudeney, Amusements in Mathematics, 1917. See problem 113, "The torn number".

Crossrefs

Supersequence of A238237.

Programs

Python

from math import isqrt
from itertools import count, islice
def ok(n):
    if n == 1: return True
    r = isqrt(n)
    if r**2 != n: return False
    s = str(n)
    return any(int(s[:i])+int(s[i:])== r for i in range(1, len(s)))
def agen(): yield from (k**2 for k in count(1) if ok(k**2))
print(list(islice(agen(), 29))) # Michael S. Branicky, Dec 29 2024

Formula

a(n) = A248353(n)^2.

Extensions

a(1)=1 prepended by Max Alekseyev, Aug 04 2017

a(27) and beyond from Michael S. Branicky, Dec 29 2024