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A069759 Frobenius number of the numerical semigroup generated by consecutive hex numbers. 1
107, 647, 2159, 5399, 11339, 21167, 36287, 58319, 89099, 130679, 185327, 255527, 343979, 453599, 587519, 749087, 941867, 1169639, 1436399, 1746359, 2103947, 2513807, 2980799, 3509999, 4106699, 4776407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 hex 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.

REFERENCES

R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = 9*n^4+36*n^3+45*n^2+18*n-1; with offset 2, a(n) = 9*n^4-9*n^2-1.

G.f.: x*(107+112*x-6*x^2+4*x^3-x^4)/(1-x)^5. - Colin Barker, Feb 14 2012

EXAMPLE

a(1)=107 because 107 is not a nonnegative linear combination of 7 and 19, but all integers greater than 107 are.

MATHEMATICA

FrobeniusNumber/@Partition[Table[3n^2+3n+1, {n, 30}], 2, 1] (* Harvey P. Dale, Dec 25 2018 *)

CROSSREFS

Cf. A003215, A037165, A059769, A069755-A069764.

Sequence in context: A142775 A200933 A142638 * A183057 A059258 A212377

Adjacent sequences:  A069756 A069757 A069758 * A069760 A069761 A069762

KEYWORD

easy,nonn

AUTHOR

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 08 2002

STATUS

approved

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Last modified August 11 03:22 EDT 2020. Contains 336421 sequences. (Running on oeis4.)