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

%I A102766 #22 Dec 29 2024 09:04:07
%S A102766 1,81,100,2025,3025,9801,10000,88209,494209,998001,1000000,4941729,
%T A102766 7441984,23804641,24502500,25502500,28005264,52881984,60481729,
%U A102766 99980001,100000000,300814336,493817284,1518037444,6049417284,6832014336,9048004641,9999800001,10000000000
%N A102766 Numbers n that can be chopped into two parts, which when added and squared result in n.
%H A102766 Michael S. Branicky, <a href="/A102766/b102766.txt">Table of n, a(n) for n = 1..131</a>
%H A102766 Henry Ernest Dudeney, <a href="https://archive.org/stream/AmusementsInMathematicspdf/AmusementsInMathematics#page/n29/mode/2up">Amusements in Mathematics</a>, 1917. See problem 113, "The torn number".
%F A102766 a(n) = A248353(n)^2.
%e A102766 a(7) = 88209 is a term as (88+209)^2 = 297^2 = 88209.
%o A102766 (Python)
%o A102766 from math import isqrt
%o A102766 from itertools import count, islice
%o A102766 def ok(n):
%o A102766     if n == 1: return True
%o A102766     r = isqrt(n)
%o A102766     if r**2 != n: return False
%o A102766     s = str(n)
%o A102766     return any(int(s[:i])+int(s[i:])== r for i in range(1, len(s)))
%o A102766 def agen(): yield from (k**2 for k in count(1) if ok(k**2))
%o A102766 print(list(islice(agen(), 29))) # _Michael S. Branicky_, Dec 29 2024
%Y A102766 Supersequence of A238237.
%K A102766 nonn,base
%O A102766 1,2
%A A102766 _Bodo Zinser_, Feb 10 2005
%E A102766 a(1)=1 prepended by _Max Alekseyev_, Aug 04 2017
%E A102766 a(27) and beyond from _Michael S. Branicky_, Dec 29 2024