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

3, 5, 9, 17, 21, 23, 25, 31, 37, 41, 43, 45, 49, 57, 61, 65, 69, 85, 89, 91, 99, 103, 107, 109, 113, 119, 121, 129, 133, 135, 143, 151, 155, 159, 163, 165, 177, 185, 187, 191, 193, 195, 201, 213, 217, 219, 231, 235, 241, 243, 247, 251, 257, 267, 269, 273, 279

Offset: 1

Author

Saish S. Kambali, Aug 11 2023

Keywords

• nonn
• easy

Comments

All terms of this sequence are odd.

A231232 lists the prime terms of this sequence.

Examples

			k = 17 is a term: 2*pi(17) + 17 = 14 + 17 = 31, a prime number.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A231232.

Programs

Maple

R:= NULL: count:= 0:
m:= 0:
for k from 1 while count < 100 do
  if isprime(k) then m:= m+1 fi;
  if isprime(2*m+k) then R:= R,k; count:= count+1 fi
od:
R; # Robert Israel, Oct 16 2023

Mathematica

Select[Range[280], PrimeQ[2*PrimePi[#] + #] &] (* Amiram Eldar, Aug 11 2023 *)

PARI

isok(k) = isprime(2*primepi(k) + k); \\ Michel Marcus, Aug 12 2023

Extensions

More terms from Jon E. Schoenfield, Aug 11 2023