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A049535
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Starts for strings of exactly 6 consecutive nonsquarefree numbers.
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11
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22020, 24647, 30923, 47672, 55447, 57120, 73447, 74848, 96675, 105772, 121667, 121847, 152339, 171348, 179972, 182347, 185247, 190447, 200848, 204323, 215303, 229172, 233223, 234375, 240424, 268223, 274547, 310120, 327424, 338920
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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Squares dividing string started by 22020 are as follows: 4, 361, 121, 9, 4, 25, respectively.
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MAPLE
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Res:= NULL:
st:= 0:
for n from 1 to 500000 do
if numtheory:-issqrfree(n) then
if st = 6 then Res:= Res, n-6 fi;
st:= 0;
else
st:= st+1;
fi
od:
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MATHEMATICA
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Select[Range[400000], !SquareFreeQ[#] && !SquareFreeQ[#+1] && !SquareFreeQ[#+2] && !SquareFreeQ[#+3] && !SquareFreeQ[#+4] && !SquareFreeQ[#+5] && SquareFreeQ[#+6]&] (* Vladimir Joseph Stephan Orlovsky, Mar 30 2011 *)
Flatten[Position[Partition[SquareFreeQ/@Range[60000], 6, 1], _?(Union[#] == {False}&), {1}, Heads->False]] (* Harvey P. Dale, May 24 2014 *)
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CROSSREFS
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The smallest members of such strings of length k are listed in A045882.
Cf. A045882 (min terms), A068781 (2-chains), A070258 (3-chains), A070284 (4-chains), A078144 (5-chains), A049535 (6-chains), A077640 (7-chains), A077647 (8-chains), A078143 (9-chains), A268313 (10-chains), A268314 (11-chains).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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