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Search: id:A069758
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| A069758 |
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Frobenius number of the numerical semigroup generated by three consecutive hexagonal numbers. |
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+0
1
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| 65, 377, 395, 797, 1589, 6029, 3347, 4571, 6035, 10997, 10979, 12212, 19409, 47246, 24023, 29003, 35357, 52112, 50603, 50411, 73049, 158207, 78155, 90203, 102005, 144443, 138467, 131474, 183077
(list; graph; listen)
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OFFSET
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2,1
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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 three consecutive hexagonal numbers are relatively prime, they generate a numerical semigroup with a Frobenius number.
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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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EXAMPLE
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a(2)=65 because 65 is not a nonnegative linear combination of 6, 15 and 28, but all integers greater than 65 are.
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CROSSREFS
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Cf. A000384, A037165, A059769, A069755-A069764.
Sequence in context: A115342 A036547 A031694 this_sequence A116678 A020292 A031421
Adjacent sequences: A069755 A069756 A069757 this_sequence A069759 A069760 A069761
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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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