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A069764
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Frobenius number of the numerical semigroup generated by consecutive octahedral numbers.
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8
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89, 773, 3611, 12179, 33349, 78889, 167383, 326471, 595409, 1027949, 1695539, 2690843, 4131581, 6164689, 8970799, 12769039, 17822153, 24441941, 32995019, 43908899, 57678389, 74872313, 96140551, 122221399, 153949249, 192262589, 238212323
(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 consecutive octahedral numbers 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
| 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
| a(n)=((1/3)n(2n^2+1)-1)((1/3)(n+1)(2(n+1)^2+1)-1)-1.
G.f.: x^2*(89+150*x+69*x^2+20*x^3-13*x^4+6*x^5-x^6)/(1-x)^7. [Colin Barker, Feb 12 2012]
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EXAMPLE
| a(2)=89 because 89 is not a nonnegative linear combination of 6 and 19 (the second and third octahedral numbers), but all integers greater than 89 are.
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CROSSREFS
| Cf. A005900, A037165, A059769, A069755-A069763.
Sequence in context: A136646 A142566 A063654 * A053580 A103548 A097155
Adjacent sequences: A069761 A069762 A069763 * A069765 A069766 A069767
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KEYWORD
| nonn,changed
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AUTHOR
| Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002
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EXTENSIONS
| More terms from Carl Najafi (carlnajafi(AT)gmail.com), Sep 10 2011
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