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Search: id:A069762
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| A069762 |
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Frobenius number of the numerical semigroup generated by three consecutive pyramidal numbers. |
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+0
2
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| 51, 191, 609, 1324, 2813, 4711, 8576, 13894, 23319, 34165, 51661, 71126, 100529, 136239, 187543, 241586, 321251, 404839, 516704, 645358
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 pyramidal 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)=51 because 51 is not a nonnegative linear combination of 5, 14 and 30, but all integers greater than 51 are.
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CROSSREFS
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Cf. A000330, A037165, A059769, A069755-A069764.
Sequence in context: A044383 A044764 A008883 this_sequence A031431 A157365 A157916
Adjacent sequences: A069759 A069760 A069761 this_sequence A069763 A069764 A069765
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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 18 2002
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