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A238334 Squares that do not contain a shorter substring that is a square.

%I A238334 #16 Feb 23 2023 11:32:07
%S A238334 0,1,4,9,25,36,576,676,5776,27556,33856,538756,586756,665856,682276,
%T A238334 763876,767376,853776,872356,2637376,2775556,2835856,5635876,6885376,
%U A238334 7376656,22886656,23755876,23775376,26275876,26687556,26873856,32672656,32878756,37527876
%N A238334 Squares that do not contain a shorter substring that is a square.
%H A238334 Giovanni Resta, <a href="/A238334/b238334.txt">Table of n, a(n) for n = 1..10000</a>
%H A238334 Michael S. Branicky, <a href="/A238334/a238334.py.txt">Python program</a>
%H A238334 Wikipedia, <a href="http://en.wikipedia.org/wiki/Substring">Substring</a>
%t A238334 fQ[n_] := Module[{d = IntegerDigits[n], len, ds, sq}, len = Length[d]; ds = FromDigits /@ Flatten[Table[Partition[d, i, 1], {i, len - 1}], 1]; sq = Select[ds, IntegerQ[Sqrt[#]] &]; sq == {}]; Select[Range[0, 10000]^2, fQ]
%o A238334 (Python) # see link for faster version for producing b-file
%o A238334 from math import isqrt
%o A238334 from itertools import count, islice
%o A238334 def issquare(n): return isqrt(n)**2 == n
%o A238334 def cond(s):
%o A238334     if len(s) == 1: return True
%o A238334     if any(d in s for d in "0149"): return False
%o A238334     ss = (s[i:i+l] for i in range(len(s)) for l in range(2, len(s)))
%o A238334     return not any(issquare(int(u)) for u in ss)
%o A238334 def agen(): yield from (k**2 for k in count(0) if cond(str(k**2)))
%o A238334 print(list(islice(agen(), 34))) # _Michael S. Branicky_, Feb 23 2023
%Y A238334 Cf. A130448.
%K A238334 nonn,base
%O A238334 1,3
%A A238334 _T. D. Noe_, Mar 05 2014