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%I #26 Nov 24 2023 13:38:19
%S 2,6,30,162,654,714,1370,1662,1722,2810,77142,156254,432974,1092242,
%T 1245230
%N Numbers k such that 2^k + 19 is prime.
%C a(14) > 5*10^5. - _Robert Price_, Aug 27 2015
%C All terms are even. - _Robert Israel_, Aug 28 2015
%C For numbers k in this sequence, the number 2^(k-1)*(2^k+19) has deficiency 20 (see A223607). - _M. F. Hasler_, Jul 18 2016
%H Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En%2B19">Search for 2^n+19</a>, PRP Top Records.
%F a(n) = 2*A253774(n). - _Joerg Arndt_, Aug 28 2015
%p select(n -> isprime(2^n+19), [seq(2*i,i=1..10000)]); # _Robert Israel_, Aug 28 2015
%t Do[ If[ PrimeQ[ 2^n + 19 ], Print[ n ] ], {n, 1, 15000} ]
%t Select[Range[10000], PrimeQ[2^# + 19] &] (* _Vincenzo Librandi_, Aug 28 2015 *)
%o (Magma) [n: n in [0..1000] | IsPrime(2^n+19)]; // _Vincenzo Librandi_, Aug 28 2015
%o (PARI) for(n=1,9e9,ispseudoprime(2^n+19)&&print1(n",")) \\ _M. F. Hasler_, Jul 18 2016
%Y Cf. A223607, A253774.
%Y Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (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), this sequence (2^k+19), A057201 (2^k+21), A057203 (2^k+23).
%K nonn,more
%O 1,1
%A _Robert G. Wilson v_, Sep 17 2000
%E a(11)-a(13) from _Robert Price_, Aug 27 2015
%E Edited by _M. F. Hasler_, Jul 18 2016
%E a(14)-a(15) found by Stefano Morozzi, added by _Elmo R. Oliveira_, Nov 19 2023
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