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%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
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