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A238334
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Squares that do not contain a shorter substring that is a square.
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4
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0, 1, 4, 9, 25, 36, 576, 676, 5776, 27556, 33856, 538756, 586756, 665856, 682276, 763876, 767376, 853776, 872356, 2637376, 2775556, 2835856, 5635876, 6885376, 7376656, 22886656, 23755876, 23775376, 26275876, 26687556, 26873856, 32672656, 32878756, 37527876
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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MATHEMATICA
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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]
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PROG
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(Python) # see link for faster version for producing b-file
from math import isqrt
from itertools import count, islice
def issquare(n): return isqrt(n)**2 == n
def cond(s):
if len(s) == 1: return True
if any(d in s for d in "0149"): return False
ss = (s[i:i+l] for i in range(len(s)) for l in range(2, len(s)))
return not any(issquare(int(u)) for u in ss)
def agen(): yield from (k**2 for k in count(0) if cond(str(k**2)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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