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Search: id:A092824
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| A092824 |
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Farey-factorial numerators. |
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+0
3
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| 1, 2, 3, 4, 6, 8, 12, 16, 18, 24, 30, 40, 48, 60, 72, 80, 90, 96, 120, 144, 180, 240, 288, 360, 432, 480, 540, 576, 600, 720, 840, 1008, 1260, 1440, 1680, 2016, 2160, 2520, 2880, 3024, 3360, 3600, 3780, 4032, 4200, 4320, 5040, 5760, 6720, 8064, 10080
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The last number in the n-th segment is n!. Let f(n) be the first number in segment n; except for initial terms, f is A001048 and A059171. Let g(n) be the second number in segment n; except for initial terms, g is A052747. Except for the initial terms, the number of numbers in segment n is given by A015614.
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FORMULA
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Let S(n) be the set of integers an!/b, where a/b ranges through the positive Farey fractions of order n. A092824 is the increasing sequence of integers in the union of the sets S(n), for n>=1.
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EXAMPLE
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The sequence begins with these segments:
1
2
3 4 6
8 12 16 18 24
For the next segment, start with these Farey
fractions of order 5:
1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/5.
Multiply these by 5! to get
30 40 48 60 72 80 90 96 120.
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CROSSREFS
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Cf. A000142, A001048, A015614, A059171, A052747.
Sequence in context: A034893 A018662 A048874 this_sequence A084094 A018718 A036451
Adjacent sequences: A092821 A092822 A092823 this_sequence A092825 A092826 A092827
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Mar 06 2004
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