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Search: id:A105392
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| A105392 |
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Frobenius number of the subsemigroup of the natural numbers generated by successive pairs of Lucas numbers. |
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+0
1
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| 0, 5, 17, 59, 169, 475, 1287, 3449, 9149, 24155, 63557, 166919, 437839, 1147645, 3006777, 7875419, 20623889, 54003395, 141397847, 370208849, 969258949, 2537616955, 6643671117, 17393524559, 45537109919, 119218140725
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Prime values of this are a(n) where n = 2, 3, 4, 8, 12, 16, 19, 28, 30. Semiprime values of this are a(n) where n = 5, 9, 10, 11, 14, 15, 20, 21, 27, 32.
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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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LINKS
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R. Jovanovic, The First 70 Lucas numbers.
Eric Weisstein's World of Mathematics, Lucas numbers.
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FORMULA
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a(n)=(L(n)-1)*(L(n+1)-1)-1 where L(n) is the n-th Lucas number A000204(n).
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EXAMPLE
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a(3) = 17 because the 3rd and 4th Lucas numbers are 4 and 7, so
a(3) = (4-1)*(7-1)-1 = 17. Or, a(3)=17 because 17 is the largest positive
integer that is not a nonnegative linear combination of 4 and 7.
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CROSSREFS
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Cf. A000204, A059769.
Adjacent sequences: A105389 A105390 A105391 this_sequence A105393 A105394 A105395
Sequence in context: A054113 A009229 A010914 this_sequence A090857 A026619 A142956
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 01 2005
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