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Search: id:A069757
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| A069757 |
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Frobenius number of the numerical semigroup generated by three consecutive pentagonal numbers. |
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+0
2
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| 43, 133, 287, 1699, 921, 1569, 3006, 3197, 4129, 12915, 6445, 8621, 14087, 13549, 16753, 43144, 20783, 25793, 38854, 35769, 43321, 101747, 48147, 57764, 82815, 74393, 89017, 198120, 93689, 108983, 151478, 133957, 159025, 341659, 162180
(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 greatest positive integer that is not a nonnegative linear combination of a_1,...,a_n. Since three consecutive pentagonal 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)=43 because 43 is not a nonnegative linear combination of 5, 12 and 22, but all integers greater than 43 are.
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CROSSREFS
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Cf. A000326, A037165, A059769, A069755-A069764.
Sequence in context: A140028 A136074 A142311 this_sequence A142394 A086760 A142412
Adjacent sequences: A069754 A069755 A069756 this_sequence A069758 A069759 A069760
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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 05 2002
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