|
Search: id:A059769
|
|
|
| A059769 |
|
Frobenius number of the subsemigroup of the natural numbers generated by successive pairs of Fibonacci numbers. |
|
+0
12
|
|
| 1, 7, 27, 83, 239, 659, 1781, 4751, 12583, 33175, 87231, 228983, 600473, 1573655, 4122467, 10796939, 28273519, 74031979, 193835949, 507497759, 1328692751, 3478637807, 9107313407, 23843452463, 62423286769, 163426800679
(list; graph; listen)
|
|
|
OFFSET
|
3,2
|
|
|
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)=(F(n)-1)*(F(n+1)-1)-1 where F(n) is the n-th Fibonacci number
|
|
EXAMPLE
|
a(3)=1 because the 3rd and 4th Fibonacci numbers are 2 and 3, so a(3)=(2-1)(3-1)-1=1. Or, a(3)=1 because 1 is the largest positive integer that is not a nonnegative linear combination of 2 and 3.
|
|
MATHEMATICA
|
Table[(Fibonacci[n]-1)(Fibonacci[n+1]-1)-1, {n, 3, 28}] - T. D. Noe (noe(AT)sspectra.com), Nov 27 2006
|
|
CROSSREFS
|
A000045.
Sequence in context: A036597 A038092 A059823 this_sequence A135914 A006350 A054485
Adjacent sequences: A059766 A059767 A059768 this_sequence A059770 A059771 A059772
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Victoria A Sapko (vsapko(AT)math.unl.edu), Feb 21 2001
|
|
EXTENSIONS
|
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 27 2006
|
|
|
Search completed in 0.002 seconds
|
