|
| |
|
|
A113188
|
|
Primes that are the difference of two Fibonacci numbers; primes in A007298.
|
|
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;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
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.
|
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n = 1..1000
|
|
|
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]
|
|
|
PROG
|
(PARI) list(lim)=my(v=List(), F=vector(A130233(lim), i, fibonacci(i)), s, t); for(i=1, #F, s=0; forstep(j=i, 1, -1, s+=F[j]; if(s>lim, break); if(isprime(s), listput(v, s)))); Set(v) \\ Charles R Greathouse IV, Oct 07 2016
|
|
|
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: A155108 A356856 A222565 * A358718 A242738 A079153
Adjacent sequences: A113185 A113186 A113187 * A113189 A113190 A113191
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
T. D. Noe, Oct 17 2005
|
|
|
STATUS
|
approved
|
| |
|
|
