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

2,1

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.

References

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

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A136074 A356727 A142311 * A354671 A365873 A142394

Adjacent sequences: A069754 A069755 A069756 * A069758 A069759 A069760

Keyword

easy,nonn

Author

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

Status

approved