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Search: id:A132468
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| A132468 |
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Longest gap between numbers relatively prime to n. |
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+0
3
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| 0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 2, 1, 1, 3, 1, 3, 2, 3, 1, 3, 1, 3, 1, 3, 1, 5, 1, 1, 2, 3, 2, 3, 1, 3, 2, 3, 1, 5, 1, 3, 2, 3, 1, 3, 1, 3, 2, 3, 1, 3, 2, 3, 2, 3, 1, 5, 1, 3, 2, 1, 2, 5, 1, 3, 2, 5, 1, 3, 1, 3, 2, 3, 2, 5, 1, 3, 1, 3, 1, 5, 2, 3, 2, 3, 1, 5, 2, 3, 2, 3, 2, 3, 1, 3, 2, 3, 1, 5, 1, 3, 4
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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Here "gap" does not include the endpoints.
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FORMULA
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a(n) = 1 at every prime power, 3 at 2^a q^b, and the unique 2 at 15.
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EXAMPLE
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E.g. n=3: the longest gap in 1, 2, 4, 5, 7, ... is 1, between 2 and 4, so a(3) = 1.
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MATHEMATICA
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a[ n_ ] := (Max[ Drop[ #, 1 ]-Drop[ #, -1 ] ]-1&)[ Select[ Range[ n+1 ], GCD[ #, n ]==1& ] ]
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CROSSREFS
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Equals A048669(n) - 1.
Sequence in context: A051997 A086869 A095345 this_sequence A090176 A102396 A095960
Adjacent sequences: A132465 A132466 A132467 this_sequence A132469 A132470 A132471
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KEYWORD
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nonn
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AUTHOR
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Michael Kleber (michael.kleber(AT)gmail.com), Nov 16 2007
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