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Search: id:A069763
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| A069763 |
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Frobenius number of the numerical semigroup generated by consecutive cubes. |
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+0
2
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| 181, 1637, 7811, 26659, 73529, 174761, 372007, 727271, 1328669, 2296909, 3792491, 6023627, 9254881, 13816529, 20114639, 28641871, 39988997, 54857141, 74070739, 98591219, 129531401, 168170617, 215970551, 274591799, 345911149
(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 consecutive cubes 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) = n^3(n+1)^3-n^3-(n+1)^3 = n^6+3n^5+3n^4-n^3-3n^2-3n-1
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EXAMPLE
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a(2)=181 because 181 is not a nonnegative linear combination of 8 and 27, but all integers greater than 181 are.
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CROSSREFS
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Cf. A000578, A037165, A059769, A069755-A069764.
Sequence in context: A067383 A107255 A137530 this_sequence A008379 A070250 A083979
Adjacent sequences: A069760 A069761 A069762 this_sequence A069764 A069765 A069766
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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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