A069759 Frobenius number of the numerical semigroup generated by consecutive hex numbers.

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

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. Fröberg, C. Gottlieb and R. Häggkvist, "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