A069757 Frobenius number of the numerical semigroup generated by three consecutive pentagonal numbers.

43, 133, 287, 1699, 921, 1569, 3006, 3197, 4129, 12915, 6445, 8621, 14087, 13549, 16753, 43144, 20783, 25793, 38854, 35769, 43321, 101747, 48147, 57764, 82815, 74393, 89017, 198120, 93689, 108983, 151478, 133957, 159025, 341659, 162180

Offset: 2

Author

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

Keywords

• easy
• nonn

Comments

The Frobenius number of a numerical semigroup generated by relatively prime integers a_1,...,a_n is the greatest positive integer that is not a nonnegative linear combination of a_1,...,a_n. Since three consecutive pentagonal numbers are relatively prime, they generate a numerical semigroup with a Frobenius number.

Examples

			a(2)=43 because 43 is not a nonnegative linear combination of 5, 12 and 22, but all integers greater than 43 are.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000
• R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).

Crossrefs

Cf. A000326, A037165, A059769, A069755-A069764.

Programs

Mathematica

FrobeniusNumber/@Partition[PolygonalNumber[5,Range[2,40]],3,1] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 16 2018 *)