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A068088
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n-3, n-2, n-1, n+1, n+2 and n+3 are squarefree.
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0
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4, 32, 36, 40, 68, 104, 108, 112, 140, 180, 184, 212, 216, 220, 256, 284, 320, 356, 392, 396, 400, 432, 436, 464, 468, 500, 544, 612, 616, 644, 680, 716, 756, 760, 788, 792, 796, 860, 896, 900, 904, 936, 940, 968, 1004, 1008, 1040, 1044, 1112, 1116, 1120, 1156, 1188, 1192, 1220, 1256, 1260, 1264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| There can not be four consecutive squarefree numbers as one of them is divisible by 2^2 =4.
From 28 to 44 there are 12 squarefree numbers among 15 consecutive integers. Other examples are 100 to 116 and 212 to 228.
The largest possible run of consecutive multiples of 4 in the sequence is 3: If n, n+4 and n+8 are in the sequence then n+4 and hence n-5 and n+13 must be divisible by 9, so neither n-4 nor n+12 can be in the sequence. - Ulrich Schimke, Apr 13, 2002
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EXAMPLE
| 36 is a term as 33,34,35 and 37,38,39 are two sets of three consecutive squarefree numbers.
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MATHEMATICA
| << NumberTheory`NumberTheoryFunctions` lst={}; Do[If[SquareFreeQ[n-1]&&SquareFreeQ[n+1]&&SquareFreeQ[n-2]&&SquareFreeQ[n+2]&&SquareFreeQ[n-3]&&SquareFreeQ[n+3], AppendTo[lst, n]], {n, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 26 2009]
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CROSSREFS
| Cf. A007675, A039833.
Sequence in context: A103909 A196247 A196250 * A118901 A114076 A078092
Adjacent sequences: A068085 A068086 A068087 * A068089 A068090 A068091
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KEYWORD
| easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 18 2002
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EXTENSIONS
| Corrected and extended by Ulrich Schimke, Apr 13, 2002. Further correction from Harvey P. Dale (hpd1(AT)nyu.edu), May 01 2002.
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