A056206 Smallest prime p such that p + 2^n is also a prime.

2, 3, 3, 3, 3, 5, 3, 3, 7, 11, 7, 5, 3, 17, 37, 3, 3, 29, 3, 53, 7, 17, 67, 11, 43, 41, 97, 29, 3, 11, 3, 11, 61, 17, 79, 53, 31, 29, 7, 23, 97, 71, 277, 29, 7, 59, 127, 5, 61, 191, 193, 101, 37, 5, 163, 3, 97, 131, 577, 131, 151, 197, 193, 29, 13, 131, 709, 3, 61

Offset: 0

Author

Labos Elemer, Oct 06 2000

Keywords

• nonn

Examples

			n=9, 512 + {2,3,5,7,11,...} = {514,515,519,523,...} = {2*257, 5*103, 11*47, 3*173, 523=prime, ...}. The smallest suitable prime is 11 and it gives 523 = 512 + 11. So a(9)=11.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2500 (first 1001 terms from T. D. Noe)

Crossrefs

Cf. A056208, A057673.

Programs

Maple

a:= proc(n) option remember; local o, p; o, p:=2^n, 2;
      while not isprime(o+p) do p:= nextprime(p) od; p
    end:
seq(a(n), n=0..75);  # Alois P. Heinz, Mar 20 2023

Mathematica

Table[i=1; While[!PrimeQ[2^n+(p=Prime[i])],i++]; p,{n,0,72}] (* Jayanta Basu, May 23 2013 *)

Formula

a(n) = Min{p|p+2^n=q, both p and q are primes}.

Extensions

a(0) from Jayanta Basu, May 23 2013