A117587 Numbers k such that 2^prime(k) - prime(k)^2 is prime.

3, 4, 7, 8, 16, 23, 49, 89, 331, 497, 1122, 11222

Offset: 1

Author

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 03 2006

Keywords

• hard
• more
• nonn

Comments

No more terms below 5000. - Giovanni Resta, Apr 03 2006

p is a prime element of the sequence A072180 iff pi(p) is a term of A117587. So since 119087 is a prime term of A072180, pi(119087)= 11222 is in the sequence. - Farideh Firoozbakht, Dec 08 2006

Examples

			4 is in the sequence because the 4th prime is 7 and 2^7 - 7^2 = 79 is a prime.
		

Crossrefs

Cf. A072180.

Programs

Maple

a:=proc(n) if isprime(2^ithprime(n)-ithprime(n)^2) then n else fi end: seq(a(n),n=1..400); # Emeric Deutsch, Apr 06 2006

Mathematica

Select[Range[1200], PrimeQ[2^# - #^2] &@ Prime@ # &] (* Michael De Vlieger, Feb 02 2019 *)

PARI

for(i=1,100,if(isprime(2^prime(i)-prime(i)^2),print1(i,",")))

Extensions

3 more terms from Giovanni Resta, Apr 03 2006

One more term from Farideh Firoozbakht, Dec 08 2006