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A238334
Squares that do not contain a shorter substring that is a square.
4
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
OFFSET
1,3
LINKS
Michael S. Branicky, Python program
Wikipedia, Substring
MATHEMATICA
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]
PROG
(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)))
print(list(islice(agen(), 34))) # Michael S. Branicky, Feb 23 2023
CROSSREFS
Cf. A130448.
Sequence in context: A087058 A046659 A063760 * A130448 A046451 A341790
KEYWORD
nonn,base
AUTHOR
T. D. Noe, Mar 05 2014
STATUS
approved