A069758 Frobenius number of the numerical semigroup generated by three consecutive hexagonal numbers.

65, 377, 395, 797, 1589, 6029, 3347, 4571, 6035, 10997, 10979, 12212, 19409, 47246, 24023, 29003, 35357, 52112, 50603, 50411, 73049, 158207, 78155, 90203, 102005, 144443, 138467, 131474, 183077

Offset

2,1

Comments

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 three consecutive hexagonal 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

Table of n, a(n) for n=2..30.

Example

a(2)=65 because 65 is not a nonnegative linear combination of 6, 15 and 28, but all integers greater than 65 are.

Mathematica

FrobeniusNumber/@Partition[Table[n(2n-1), {n, 2, 35}], 3, 1] (* Harvey P. Dale, Jul 25 2011 *)

Crossrefs

Cf. A000384, A037165, A059769, A069755-A069764.

Sequence in context: A319617 A300162 A211259 * A116678 A218845 A219424

Adjacent sequences: A069755 A069756 A069757 * A069759 A069760 A069761

Keyword

easy,nonn

Author

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 08 2002

Status

approved