|
Search: id:A113188
|
|
|
| A113188 |
|
Primes that are the difference of two Fibonacci numbers; primes in A007298. |
|
+0
12
|
|
| 2, 3, 5, 7, 11, 13, 19, 29, 31, 47, 53, 89, 131, 139, 199, 233, 521, 607, 953, 1453, 1597, 2207, 2351, 2579, 3571, 6763, 9349, 10891, 28513, 28649, 28657, 42187, 44771, 46279, 75017, 189653, 317777, 514229, 1981891, 2177699, 3010349, 3206767
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The difference F(i)-F(j) equals the sum F(j-1)+...+F(i-2) [Corrected by Patrick Capelle, Mar 01 2008]. In general, we need gcd(i,j)=1 for F(i)-F(j) to be prime. The exceptions are handled by the following rule: if i and j are both even or both odd, then F(i)-F(j) is prime if either (1) i-j=4 and L(i-2) is a Lucas prime or (2) i-j=2 and F(i-1) is a Fibonacci prime.
|
|
EXAMPLE
|
The prime 139 is here because it is F(12)-F(5).
|
|
MATHEMATICA
|
lst={}; Do[p=Fibonacci[n]-Fibonacci[i]; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 40}, {i, n-1}]; Union[lst]
|
|
CROSSREFS
|
Cf. A000045 (Fibonacci numbers), A001605 (Fibonacci(n) is prime), A001606 (Lucas(n) is prime), A113189 (number of times that Fibonacci(n)-Fibonacci(i) is prime for i=0..n-3).
Sequence in context: A020588 A114111 A155108 this_sequence A079153 A020616 A067910
Adjacent sequences: A113185 A113186 A113187 this_sequence A113189 A113190 A113191
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Oct 17 2005
|
|
|
Search completed in 0.002 seconds
|
