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Search: id:A078143
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| A078143 |
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Smallest term of a run of at least 9 consecutive integers which are not square-free. |
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5
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| 8870024, 33908368, 49250144, 69147868, 70918820, 111500620, 112931372, 164786748, 167854344, 200997948, 203356712, 207543320, 211014920, 216785256, 221167422, 221167423, 221167424, 236645624, 240574368, 262315467, 262315468
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OFFSET
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1,1
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COMMENT
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The sequence includes an infinite family of arithmetic progressions. Such AP's can be constructed to each term, with large differences [like squares of primorials, A061742(7)]. It is necessary to solve suitable systems of linear Diophantine equations. E.g.: arithmetic progression subsequences of starting 9-chains is {mk+69147868+j} where j=0..8, m=510510^2 because square prime factors of a(4)+j=68147868+j are 4, 49, 121, 169, 4, 9, 289, 25, 4 resp. for j=0..8; k goes to infinity; 7th primorial is sufficient, 9th is not necessary.Construction is provable for arbitrary long [>9] chains. - Labos E. (labos(AT)ana.sote.hu), Nov 25 2002
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MATHEMATICA
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s9[x_] := Apply[Plus, Table[Abs[MoebiusMu[x+j]], {j, 0, 8}]]; Do[If[Equal[s9[n], 0], Print[n]], {n, 8000000, 1000000000}]
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CROSSREFS
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Cf. A013929, A045882, A049535, A051681, A077640, A077647.
Cf. A049535, A077647, A078143.
Sequence in context: A141137 A015378 A151936 this_sequence A141645 A151933 A162021
Adjacent sequences: A078140 A078141 A078142 this_sequence A078144 A078145 A078146
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 22 2002
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EXTENSIONS
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a(6)-a(21) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 26 2008
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