A057200 - OEIS

%I #35 Nov 24 2023 13:38:29

%S 1,13,21,33,81,129,285,297,769,3381,4441,7065,77121,133437,184189,

%T 191745,1279921

%N Numbers k such that 2^k + 17 is prime.

%C a(17) > 5*10^5. - _Robert Price_, Oct 05 2015

%C For numbers k in this sequence, 2^(k-1)*(2^k+17) has deficiency 18 (see A223608). - _M. F. Hasler_, Jul 18 2016

%C All terms are odd. - _Elmo R. Oliveira_, Nov 19 2023

%H Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En%2B17">Search for 2^n+17</a>, PRP Top Records.

%t Do[ If[ PrimeQ[ 2^n + 17 ], Print[ n ]], {n, 0, 11811} ]

%t Select[Range[10000], PrimeQ[2^# + 17] &] (* _Vincenzo Librandi_, Aug 28 2015 *)

%o (Magma) [n: n in [0..1000] | IsPrime(2^n+17)]; // _Vincenzo Librandi_, Aug 28 2015

%o (PARI) is(n)=isprime(2^n+17) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A223608.

%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), this sequence (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23).

%K nonn,more

%O 1,2

%A _Robert G. Wilson v_, Sep 16 2000

%E a(13)-a(16) from _Robert Price_, Aug 24 2015

%E Edited by _M. F. Hasler_, Jul 18 2016

%E a(17) found by Stefano Morozzi, added by _Elmo R. Oliveira_, Nov 19 2023