A094366 a(n) is the number of two-generated numerical semigroups whose Frobenius number is 2n-1.

1, 1, 2, 2, 1, 3, 2, 1, 3, 3, 1, 4, 2, 2, 4, 3, 1, 3, 2, 2, 4, 3, 1, 5, 3, 2, 4, 3, 1, 6, 2, 2, 4, 3, 2, 6, 2, 1, 3, 5, 1, 6, 2, 2, 6, 3, 1, 5, 3, 2, 4, 4, 1, 6, 4, 3, 4, 2, 1, 7, 2, 2, 5, 4, 2, 6, 2, 1, 4, 6, 1, 7, 2, 2, 6, 4, 2, 5, 2, 3, 4, 3, 1, 8, 4, 2, 4, 4, 1, 9, 4, 2, 4, 3, 2, 7, 2, 2, 6, 6, 1, 5, 2, 3, 7

Offset: 1

Author

Corina Flynn (Corinamachina(AT)hotmail.com), May 07 2004

Keywords

• easy
• nonn

Comments

A numerical semigroup is a set of natural numbers closed under addition. Its Frobenius number is the largest number not in it. In the case of a semigroup generated by two relatively prime numbers a and b, its Frobenius number is ab-a-b, which is always odd.

Examples

			a(9) = 3: the 3 semigroups generated by {2, 19}, {3, 10} and {4, 7} have Frobenius number 17.
		

Links

• David Wasserman, Table of n, a(n) for n = 1..300
• J. C. Rosales, P. A. Garcia-Sanchez and J. I. Garcia-Garcia, Every positive integer is the Frobenius number of a numerical semigroup with three generators, Math. Scand. 94 (2004), no. 1, 5-12.

Crossrefs

Cf. A094365, A094367.

Extensions

Edited and extended by David Wasserman, Sep 27 2006