A057663 Primes p such that p + 2^p is also a prime.

3, 5, 89, 317, 701

Offset: 1

Author

Labos Elemer, Oct 16 2000

Keywords

• nonn
• hard
• more

Comments

Different from A056206, where, e.g., at n=89, 89 is not minimal, A056206(89)=29 and not 89.

a(6) > 27479. - Ralf Stephan, Oct 23 2002

Intersection of A000040 and A052007. - Iain Fox, Nov 08 2017

a(6) > 678561. - Iain Fox, Nov 08 2017

Every term other than 3 is congruent to 5 (mod 6). - Arkadiusz Wesolowski, Nov 14 2017

These terms satisfy phi(k + 2^k) = phi(k) + 2^k, where phi is A000010, the Euler totient function. Conjecture: this sequence gives all numbers k that satisfy the condition phi(k + 2^k) = phi(k) + 2^k. - Juri-Stepan Gerasimov, May 23 2019

Examples

			q=3, 2^3 + 3 = 11 a prime.
		

Crossrefs

Cf. A000010, A006127, A056206, A056208, A057664, A057665.

Programs

Magma

[p: p in PrimesUpTo(1000) | IsPrime(2^p+p) ] // Vincenzo Librandi, Aug 07 2010

Mathematica

Select[Prime@ Range[10^3], PrimeQ[# + 2^#] &] (* Michael De Vlieger, Nov 08 2017 *)

PARI

lista(nn) = forprime(p=3, nn, if(ispseudoprime(p + 2^p), print1(p, ", "))) \\ Iain Fox, Nov 13 2017

Sage

[n for n in (1..1000) if is_prime(n) and is_prime(2^n+n)] # G. C. Greubel, May 24 2019