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
KEYWORD
easy,nonn
AUTHOR
Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 05 2002
STATUS
approved