|
Search: id:A069760
|
|
|
| A069760 |
|
Frobenius number of the numerical semigroup generated by consecutive centered square numbers. |
|
+0
1
|
|
| 47, 287, 959, 2399, 5039, 9407, 16127, 25919, 39599, 58079, 82367, 113567, 152879, 201599, 261119, 332927, 418607, 519839, 638399, 776159, 935087, 1117247, 1324799, 1559999, 1825199, 2122847
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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 consecutive centered squares are relatively prime, they generate a numerical semigroup with a Frobenius number. The Frobenius number of a 2-generator semigroup <a,b> is ab-a-b.
|
|
REFERENCES
|
R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
|
|
FORMULA
|
a(n) = 4n^4+16n^3+20n^2+8n-1
|
|
EXAMPLE
|
a(1)=47 because 47 is not a nonnegative linear combination of 5 and 13, but all integers greater than 47 are.
|
|
CROSSREFS
|
Cf. A001844, A037165, A059769, A069755-A069764.
Sequence in context: A142119 A142164 A142774 this_sequence A140043 A074774 A107611
Adjacent sequences: A069757 A069758 A069759 this_sequence A069761 A069762 A069763
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 09 2002
|
|
|
Search completed in 0.002 seconds
|
