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%I #23 Nov 28 2023 12:53:26
%S 1,3,5,7,9,15,23,29,31,55,71,77,297,573,1301,1555,1661,4937,5579,6191,
%T 6847,6959,19985,26285,47093,74167,149039,175137,210545,240295,306153,
%U 326585,345547
%N Numbers k such that 2^k + 11 is prime.
%C a(34) > 5*10^5. - _Robert Price_, Aug 26 2015
%C For numbers k in this sequence, 2^(k-1)*(2^k+11) has deficiency 12 (see A141549). All terms are odd since 4^n+11 == 1+2 == 0 (mod 3). - _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%2B11">Search for 2^n+11</a>, PRP Top Records.
%H Lei Zhou, <a href="http://www.bme.emory.edu/~lzhou/prime/">Between 2^n and primes</a>. [broken link]
%e k = 1: 2^1 + 11 = 13 is prime.
%e k = 3: 2^3 + 11 = 19 is prime.
%e k = 2: 2^2 + 11 = 15 is not prime.
%t Do[ If[ PrimeQ[2^n + 11], Print[n]], {n, 15250}] (* _Robert G. Wilson v_, Jan 21 2005 *)
%o (PARI) for(n=1,9e9,ispseudoprime(2^n+11)&&print1(n",")) \\ _M. F. Hasler_, Jul 18 2016
%Y Cf. A094076, A141549.
%Y Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), A057196(2^k+9), this sequence (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 _Lei Zhou_, Jan 20 2005
%E a(18)-a(22) from _Robert G. Wilson v_, Jan 21 2005
%E a(23)-a(33) from _Robert Price_, Dec 06 2013
%E Edited by _M. F. Hasler_, Jul 18 2016