%I #16 Jun 11 2021 18:22:59
%S 61,2,11,67,149,2081,5651,11831,51479,536279,3058871,11894801,
%T 106446433
%N a(n) is the least prime p such that there are exactly n primes of the form p+2^k for 2^k < p.
%F A345238(A000720(a(n))) = n.
%e a(3) = 67 because 67+2^2 = 71, 67+2^4 = 83 and 67+2^6 = 131 are primes, and 67 is the least prime that produces exactly 3 primes in this way.
%p f:= proc(p) local k;
%p nops(select(isprime, [seq(p+2^k,k=1..ilog2(p))]))
%p end proc:
%p f(2):= 1
%p V:= Array(0..11):
%p count:= 0:
%p p:= 1:
%p while count < 12 do
%p p:= nextprime(p);
%p v:= f(p);
%p if V[v] = 0 then V[v]:= p; count:= count+1
%p fi
%p od:
%p convert(V,list);
%t Table[p=1;While[Length@Select[Table[Prime@p+2^k,{k,0,Floor[Log2@Prime@p]}],PrimeQ]!=n,p++];Prime@p,{n,0,9}] (* _Giorgos Kalogeropoulos_, Jun 11 2021 *)
%Y Cf. A000720, A345238.
%K nonn,more
%O 0,1
%A _J. M. Bergot_ and _Robert Israel_, Jun 11 2021