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

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

1,2

Links

Max Alekseyev, Table of n, a(n) for n = 1..10000 (terms for n = 1..131 from Michael S. Branicky)

Henry Ernest Dudeney, Amusements in Mathematics, 1917. See problem 113, "The torn number".

Formula

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

Example

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

Prog

(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

Crossrefs

Supersequence of A238237.

Sequence in context: A067521 A117686 A104113 * A380428 A256349 A202002

Adjacent sequences: A102763 A102764 A102765 * A102767 A102768 A102769

Keyword

nonn,base

Author

Bodo Zinser, Feb 10 2005

Extensions

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

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

Status

approved