2,1

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 squares 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.

a(n+1)=Numerator of ((n + 2)! - (n - 2)!)/(n!) n=2,3,4,5,... - Artur Jasinski (grafix(AT)csl.pl), Jan 09 2007

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

a(n) = n^2*(n+1)^2-n^2-(n+1)^2 = n^4+2n^3-n^2-2n-1

Table[Numerator[((n + 2)! - (n - 2)!)/(n!)], {n, 2, 20}] - Artur Jasinski (grafix(AT)csl.pl), Jan 09 2007

a(2)=23 because 23 is not a nonnegative linear combination of 4 and 9, but all integers greater than 23 are.

Table[(n^2-1)((n+1)^2-1)-1, {n, 2, 30}] - T. D. Noe (noe(AT)sspectra.com), Nov 27 2006

Cf. A000290, A037165, A059769, A069755, A069757-A069764.

Adjacent sequences: A069753 A069754 A069755 this_sequence A069757 A069758 A069759

Sequence in context: A057877 A042026 A042028 this_sequence A099068 A044355 A044736

easy,nice,nonn

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 05 2002

Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 27 2006