A059242 Numbers k such that 2^k + 5 is prime.

1, 3, 5, 11, 47, 53, 141, 143, 191, 273, 341, 16541, 34001, 34763, 42167, 193965, 282203

Offset: 1

Author

Tony Davie (ad(AT)dcs.st-and.ac.uk), Jan 21 2001

Keywords

• nonn
• hard
• more

Comments

The subsequence of primes starts 3, 5, 11, 47, 53, 191, ... - Vincenzo Librandi, Aug 07 2010

For k in this sequence, 2^(k-1)*(2^k+5) is in A141548: numbers of deficiency 6. - M. F. Hasler, Apr 23 2015

a(18) > 5*10^5. - Robert Price, Aug 23 2015

a(18) > 6*10^5. - Tyler NeSmith, Jan 18 2021

All terms are odd - Elmo R. Oliveira, Dec 01 2023

Examples

			2^3 + 5 = 13 is prime, but 2^4 + 5 = 21 is not.
		

Links

• Keith Conrad, Square patterns and infinitude of primes, University of Connecticut, 2019.
• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n+5, PRP Top Records.

Crossrefs

Cf. A094076, A141548.

Cf. A019434 (primes 2^k+1), A057732 (2^k+3), this sequence (2^k+5), A057195 (2^k+7), A057196 (2^k+9), A102633 (2^k+11), A102634 (2^k+13), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23).

Programs

Mathematica

Select[Range[20000],PrimeQ[2^#+5]&] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011 *)

PARI

is(n)=ispseudoprime(2^n+5) \\ M. F. Hasler, Apr 23 2015

Extensions

More terms from Santi Spadaro, Oct 04 2002

a(12) from Hans Havermann, Oct 07 2002

a(13)-a(15) from Charles R Greathouse IV, Oct 07 2011

a(16)-a(17) from Robert Price, Dec 06 2013