A069762 Frobenius number of the numerical semigroup generated by three consecutive pyramidal numbers.

51, 191, 609, 1324, 2813, 4711, 8576, 13894, 23319, 34165, 51661, 71126, 100529, 136239, 187543, 241586, 321251, 404839, 516704, 645358, 813141, 982651, 1221299, 1463734, 1767473, 2106271, 2524101, 2940909, 3500209, 4061663, 4736456, 5474526, 6352219, 7228469

Offset: 2

Author

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002

Keywords

• easy
• nonn

Comments

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 three consecutive pyramidal numbers are relatively prime, they generate a numerical semigroup with a Frobenius number.

Examples

			a(2)=51 because 51 is not a nonnegative linear combination of 5, 14 and 30, but all integers greater than 51 are.
		

Links

• R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).

Crossrefs

Cf. A000330, A037165, A059769, A069755-A069764.

Extensions

More terms from and offset corrected by Sean A. Irvine, May 19 2024