Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #46 Dec 01 2023 19:52:09
%S 1,3,5,11,47,53,141,143,191,273,341,16541,34001,34763,42167,193965,
%T 282203
%N Numbers k such that 2^k + 5 is prime.
%C The subsequence of primes starts 3, 5, 11, 47, 53, 191, ... - _Vincenzo Librandi_, Aug 07 2010
%C For k in this sequence, 2^(k-1)*(2^k+5) is in A141548: numbers of deficiency 6. - _M. F. Hasler_, Apr 23 2015
%C a(18) > 5*10^5. - _Robert Price_, Aug 23 2015
%C a(18) > 6*10^5. - _Tyler NeSmith_, Jan 18 2021
%C All terms are odd - _Elmo R. Oliveira_, Dec 01 2023
%H Keith Conrad, <a href="https://kconrad.math.uconn.edu/blurbs/ugradnumthy/squaresandinfmanyprimes.pdf">Square patterns and infinitude of primes</a>, University of Connecticut, 2019.
%H Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En%2B5">Search for 2^n+5</a>, PRP Top Records.
%e 2^3 + 5 = 13 is prime, but 2^4 + 5 = 21 is not.
%t Select[Range[20000],PrimeQ[2^#+5]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2011 *)
%o (PARI) is(n)=ispseudoprime(2^n+5) \\ _M. F. Hasler_, Apr 23 2015
%Y Cf. A094076, A141548.
%Y 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).
%K nonn,hard,more
%O 1,2
%A Tony Davie (ad(AT)dcs.st-and.ac.uk), Jan 21 2001
%E More terms from Santi Spadaro, Oct 04 2002
%E a(12) from _Hans Havermann_, Oct 07 2002
%E a(13)-a(15) from _Charles R Greathouse IV_, Oct 07 2011
%E a(16)-a(17) from _Robert Price_, Dec 06 2013