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A364877 Numbers k such that 2*pi(k) + k is a prime number.

%I A364877 #40 Oct 16 2023 23:26:19
%S A364877 3,5,9,17,21,23,25,31,37,41,43,45,49,57,61,65,69,85,89,91,99,103,107,
%T A364877 109,113,119,121,129,133,135,143,151,155,159,163,165,177,185,187,191,
%U A364877 193,195,201,213,217,219,231,235,241,243,247,251,257,267,269,273,279
%N A364877 Numbers k such that 2*pi(k) + k is a prime number.
%C A364877 All terms of this sequence are odd.
%C A364877 A231232 lists the prime terms of this sequence.
%H A364877 Robert Israel, <a href="/A364877/b364877.txt">Table of n, a(n) for n = 1..10000</a>
%e A364877 k = 17 is a term: 2*pi(17) + 17 = 14 + 17 = 31, a prime number.
%p A364877 R:= NULL: count:= 0:
%p A364877 m:= 0:
%p A364877 for k from 1 while count < 100 do
%p A364877   if isprime(k) then m:= m+1 fi;
%p A364877   if isprime(2*m+k) then R:= R,k; count:= count+1 fi
%p A364877 od:
%p A364877 R; # _Robert Israel_, Oct 16 2023
%t A364877 Select[Range[280], PrimeQ[2*PrimePi[#] + #] &] (* _Amiram Eldar_, Aug 11 2023 *)
%o A364877 (PARI) isok(k) = isprime(2*primepi(k) + k); \\ _Michel Marcus_, Aug 12 2023
%Y A364877 Cf. A000720, A231232.
%K A364877 nonn,easy
%O A364877 1,1
%A A364877 _Saish S. Kambali_, Aug 11 2023
%E A364877 More terms from _Jon E. Schoenfield_, Aug 11 2023