A056206 - OEIS

%I #24 Mar 20 2023 12:49:08

%S 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,

%T 3,11,3,11,61,17,79,53,31,29,7,23,97,71,277,29,7,59,127,5,61,191,193,

%U 101,37,5,163,3,97,131,577,131,151,197,193,29,13,131,709,3,61

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

%H Alois P. Heinz, <a href="/A056206/b056206.txt">Table of n, a(n) for n = 0..2500</a> (first 1001 terms from T. D. Noe)

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

%e 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.

%p a:= proc(n) option remember; local o, p; o, p:=2^n, 2;

%p       while not isprime(o+p) do p:= nextprime(p) od; p

%p     end:

%p seq(a(n), n=0..75);  # _Alois P. Heinz_, Mar 20 2023

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

%Y Cf. A056208, A057673.

%K nonn

%O 0,1

%A _Labos Elemer_, Oct 06 2000

%E a(0) from _Jayanta Basu_, May 23 2013