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Search: id:A069759
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| A069759 |
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Frobenius number of the numerical semigroup generated by consecutive hex numbers. |
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+0
1
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| 107, 647, 2159, 5399, 11339, 21167, 36287, 58319, 89099, 130679, 185327, 255527, 343979, 453599, 587519, 749087, 941867, 1169639, 1436399, 1746359, 2103947, 2513807, 2980799, 3509999, 4106699, 4776407
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The Frobenius number of a numerical semigroup generated by relatively prime integers a_1,...,a_n is the largest positive integer that is not a nonnegative linear combination of a_1,...,a_n. Since consecutive hex numbers are relatively prime, they generate a numerical semigroup with a Frobenius number. The Frobenius number of a 2-generated semigroup <a,b> has the formula ab-a-b.
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REFERENCES
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R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
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FORMULA
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a(n) = 9*n^4+36*n^3+45*n^2+18*n-1; with offset 2, a(n) = 9*n^4-9*n^2-1
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EXAMPLE
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a(1)=107 because 107 is not a nonnegative linear combination of 7 and 19, but all integers greater than 107 are.
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CROSSREFS
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Cf. A003215, A037165, A059769, A069755-A069764.
Sequence in context: A142696 A142775 A142638 this_sequence A059258 A113932 A114356
Adjacent sequences: A069756 A069757 A069758 this_sequence A069760 A069761 A069762
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KEYWORD
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easy,nonn
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AUTHOR
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Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 08 2002
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