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a(n) is the least prime p such that there are exactly n primes of the form p+2^k for 2^k < p.
1

%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