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Search: id:A094366
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| A094366 |
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a(n) is the number of two-generated numerical semigroups whose Frobenius number is 2n-1. |
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+0
3
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| 1, 1, 2, 2, 1, 3, 2, 1, 3, 3, 1, 4, 2, 2, 4, 3, 1, 3, 2, 2, 4, 3, 1, 5, 3, 2, 4, 3, 1, 6, 2, 2, 4, 3, 2, 6, 2, 1, 3, 5, 1, 6, 2, 2, 6, 3, 1, 5, 3, 2, 4, 4, 1, 6, 4, 3, 4, 2, 1, 7, 2, 2, 5, 4, 2, 6, 2, 1, 4, 6, 1, 7, 2, 2, 6, 4, 2, 5, 2, 3, 4, 3, 1, 8, 4, 2, 4, 4, 1, 9, 4, 2, 4, 3, 2, 7, 2, 2, 6, 6, 1, 5, 2, 3, 7
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OFFSET
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1,3
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COMMENT
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A numerical semigroup is a set of natural numbers closed under addition. Its Frobenius number is the largest number not in it. In the case of a semigroup generated by two relatively prime numbers a and b, its Frobenius number is ab-a-b, which is always odd.
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REFERENCES
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J. C. Rosales, P. A. Garcia-Sanchez and J. I. Garcia-Garcia, Every positive integer is the Frobenius number of a numerical semigroup with three generators, Math. Scand. 94 (2004), no. 1, 5-12.
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LINKS
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David Wasserman, Table of n, a(n) for n = 1..300
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EXAMPLE
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a(9) = 3: the 3 semigroups generated by {2, 19}, {3, 10} and {4, 7} have Frobenius number 17.
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CROSSREFS
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Cf. A094365, A094367.
Adjacent sequences: A094363 A094364 A094365 this_sequence A094367 A094368 A094369
Sequence in context: A069004 A053274 A026146 this_sequence A124018 A111709 A039996
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KEYWORD
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easy,nonn
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AUTHOR
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Corina Flynn (Corinamachina(AT)hotmail.com), May 07 2004
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EXTENSIONS
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Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), Sep 27 2006
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