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A069761
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Frobenius number of the numerical semigroup generated by four consecutive tetrahedral numbers.
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1
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41, 249, 253, 853, 1243, 1571, 2619, 5059, 5357, 9437, 11801, 13609, 18327, 27607, 28919, 41951, 49169, 54473, 67253, 90573, 94051, 124099, 140347, 152027, 178989, 226141, 233369, 291089, 321839, 343639, 392631, 475999, 488993, 587633, 639653, 676181, 756779
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| 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 four consecutive tetrahedral numbers are relatively prime, they generate a numerical semigroup with a Frobenius number.
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REFERENCES
| 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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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 2..100
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EXAMPLE
| a(2)=41 because 41 is not a nonnegative linear combination of 4, 10, 20 and 35, but all integers greater than 43 are.
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MATHEMATICA
| FrobeniusNumber/@Partition[Binomial[Range[2, 50]+2, 3], 4, 1] (* From Harvey P. Dale, Jan 22 2012 *)
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CROSSREFS
| Cf. A000292, A037165, A059769, A069755-A069764.
Sequence in context: A098675 A056213 A068707 * A140634 A140848 A063939
Adjacent sequences: A069758 A069759 A069760 * A069762 A069763 A069764
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KEYWORD
| easy,nonn
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AUTHOR
| Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 09 2002
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EXTENSIONS
| Sequence terms corrected and extended by Harvey P. Dale, Jan 22 2012
Offset corrected and example corrected by Harvey P. Dale, Jan 24 2012
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