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Numbers k such that 2^k + 33 is prime.
8

%I #38 Nov 27 2023 15:07:05

%S 2,3,6,11,12,14,15,20,30,60,68,75,108,116,135,206,210,410,446,558,851,

%T 1482,1499,2039,2051,4196,7046,7155,8735,10619,18420,20039,46719,

%U 75348,179790,203018,434246

%N Numbers k such that 2^k + 33 is prime.

%C Some terms correspond to probable primes. Lifchitz link shows the terms 179790 found by _Donovan Johnson_ and 203018 by Lelio R Paula. - _Jens Kruse Andersen_, Sep 30 2014

%C a(38) > 5*10^5. - _Robert Price_, Nov 07 2015

%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=2^n%2B33">Search for 2^n+33</a>, PRP Top Records.

%p A247957:=n->`if`(isprime(2^n+33),n,NULL): seq(A247957(n), n=0..1000); # _Wesley Ivan Hurt_, Sep 28 2014

%t Select[Range[10000], PrimeQ[2^# + 33] &]

%o (Magma) /* The code gives only the terms up to 851: */ [n: n in [1..1400]| IsPrime( 2^n + 33 )];

%o (PARI) is(n)=ispseudoprime(2^n+33) \\ _Charles R Greathouse IV_, Feb 20 2017

%Y Cf. A094076, A176926, A247957.

%Y Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1; A057732 (d=3), A059242 (d=5), A057195 (d=7), A057196 (d=9), A102633 (d=11), A102634 (d=13), A057197 (d=15), A057200 (d=17), A057221 (d=19), A057201 (d=21), A057203 (d=23), A157006 (d=25), A157007 (d=27), A156982 (d=29), A247952 (d=31), this sequence (d=33), A220077 (d=35).

%K nonn,more

%O 1,1

%A _Vincenzo Librandi_, Sep 28 2014

%E a(30)-a(34) from _Jens Kruse Andersen_, Sep 30 2014

%E a(35)-a(36) (discovered by _Donovan Johnson_ and Lelio R Paula, respectively; see the Lifchitz link) added by _Robert Price_, Oct 04 2015

%E a(37) from _Robert Price_, Nov 07 2015