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A069757
Frobenius number of the numerical semigroup generated by three consecutive pentagonal numbers.
2
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
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