

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
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OFFSET

1,1


COMMENTS

The difference F(i)F(j) equals the sum F(j1)+...+F(i2) [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) ij=4 and L(i2) is a Lucas prime or (2) ij=2 and F(i1) 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, n1}]; 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..n3).
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



