A069761 Frobenius number of the numerical semigroup generated by four consecutive tetrahedral numbers.

41, 249, 253, 853, 1243, 1571, 2619, 5059, 5357, 9437, 11801, 13609, 18327, 27607, 28919, 41951, 49169, 54473, 67253, 90573, 94051, 124099, 140347, 152027, 178989, 226141, 233369, 291089, 321839, 343639, 392631, 475999, 488993, 587633, 639653, 676181, 756779

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 four consecutive tetrahedral 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..100

Example

a(2)=41 because 41 is not a nonnegative linear combination of 4, 10, 20 and 35, but all integers greater than 43 are.

Mathematica

FrobeniusNumber/@Partition[Binomial[Range[2, 50]+2, 3], 4, 1] (* Harvey P. Dale, Jan 22 2012 *)

Crossrefs

Cf. A000292, A037165, A059769, A069755-A069764.

Sequence in context: A098675 A056213 A068707 * A322241 A140634 A140848

Adjacent sequences: A069758 A069759 A069760 * A069762 A069763 A069764

Keyword

easy,nonn

Author

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 09 2002

Extensions

Sequence terms corrected and extended by Harvey P. Dale, Jan 22 2012

Offset corrected and example corrected by Harvey P. Dale, Jan 24 2012

Status

approved