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A056208 Primes p+2^n arising in A056206.

%I A056208 #10 Jun 09 2020 07:21:39
%S A056208 3,5,7,11,19,37,67,131,263,523,1031,2053,4099,8209,16421,32771,65539,
%T A056208 131101,262147,524341,1048583,2097169,4194371,8388619,16777259,
%U A056208 33554473,67108961,134217757,268435459,536870923,1073741827,2147483659
%N A056208 Primes p+2^n arising in A056206.
%H A056208 Robert Israel, <a href="/A056208/b056208.txt">Table of n, a(n) for n = 0..2000</a>
%e A056208 n=13, 2^13+p=8192+p is not prime for p=2,3,5,7,11,13. At first, for p=17, 8209 is prime; Primes obtained also for many larger p, the next is 8221. So a(13)=8209, the smallest one.
%p A056208 f:= proc(n) local p,q,t;
%p A056208   t:= 2^n; p:= 1;
%p A056208   do
%p A056208     p:= nextprime(p);
%p A056208     q:= p+t;
%p A056208     if isprime(q) then return q fi
%p A056208   od
%p A056208 end proc:
%p A056208 map(f, [$0..50]); # _Robert Israel_, Aug 22 2019
%t A056208 a[n_] := Module[{p = 1, q, t = 2^n}, While[True, p = NextPrime[p]; q = p+t; If[PrimeQ[q], Return[q]]]];
%t A056208 a /@ Range[0, 50] (* _Jean-François Alcover_, Jun 09 2020, after Maple *)
%Y A056208 Cf. A056206.
%K A056208 nonn
%O A056208 0,1
%A A056208 _Labos Elemer_, Oct 06 2000
%E A056208 a(0)=3 inserted by _Robert Israel_, Aug 22 2019