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

2,1

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.

Links

Table of n, a(n) for n=2..35.

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

Example

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

Crossrefs

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

Sequence in context: A353599 A008883 A327624 * A245829 A369922 A031431

Adjacent sequences: A069759 A069760 A069761 * A069763 A069764 A069765

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved