

A069758


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


0



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
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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), 6383 (for definition of Frobenius number).


LINKS



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(2n1), {n, 2, 35}], 3, 1] (* Harvey P. Dale, Jul 25 2011 *)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR

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


STATUS

approved



