A178576 Primes that are the sum of two Fibonacci numbers.

2, 3, 5, 7, 11, 13, 23, 29, 37, 47, 89, 97, 149, 157, 199, 233, 241, 379, 521, 613, 631, 1021, 1597, 1741, 2207, 3571, 9349, 10949, 11933, 17713, 28657, 46381, 46457, 46601, 50549, 75169, 196439, 203183, 214129, 514229, 560597, 832129, 2178343

Offset: 1

Author

Carmine Suriano, Jan 12 2011

Keywords

• nonn

Comments

The corresponding prime indices are in A178971.

Examples

			Prime 613 can be expressed as 3+610 = Fibonacci(4)+Fibonacci(15), therefore 613 is in the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..5624

Crossrefs

Cf. A000040, A000045, A178971. Subsequence of A059389.

Programs

Mathematica

f=Fibonacci[Range[33]]; Select[Union[Flatten[Outer[Plus, f, f]]], PrimeQ]

PARI

list(lim)={
    my(v,u=List(),t);
    v=vector(log(lim*sqrt(5))\log((1+sqrt(5))/2)+1,n,fibonacci(n));
    for(i=1,#v,for(j=i+1,#v,
        t = v[i] + v[j];
        if(t > lim, break);
        if(ispseudoprime(t),listput(u, t))
    ));
    vecsort(Vec(u),,8)
}; \\ Charles R Greathouse IV, Jul 23 2012