|
|
A069762
|
|
Frobenius number of the numerical semigroup generated by three consecutive pyramidal numbers.
|
|
1
|
|
|
51, 191, 609, 1324, 2813, 4711, 8576, 13894, 23319, 34165, 51661, 71126, 100529, 136239, 187543, 241586, 321251, 404839, 516704, 645358
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
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 pyramidal 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)=51 because 51 is not a nonnegative linear combination of 5, 14 and 30, but all integers greater than 51 are.
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002
|
|
STATUS
|
approved
|
|
|
|