%I A091516
%S A091516 7,47,223,3967,16127,1046527,16769023,1073676287,68718952447,
%T A091516 274876858367,4398042316799,1125899839733759,18014398241046527,
%U A091516 1298074214633706835075030044377087
%N A091516 Carol primes 4^n-2^{n+1}-1.
%C A091516 There are only 25 such primes below 4^1000. Terms beyond a(15) are too 
               large to be displayed here: The sequence should be extended by listing 
               the corresponding n-values in A091515. - M. F. Hasler (www.univ-ag.fr/
               ~mhasler), May 15 2008
%C A091516 Is there an explanation for the following observed pattern? Between groups 
               of primes of roughly the same size, there is a gap of about the magnitude 
               of these primes, i.e. the size roughly doubles (e.g. after the 16-17 
               digit primes, there is a 34 digit prime, then an 78 digit prime and 
               some others up to 105 digits, then some 200-250 digit primes, then 
               approximately 500 digits...). - M. F. Hasler (www.univ-ag.fr/~mhasler), 
               May 15 2008
%H A091516 M. F. Hasler, <a href="b091516.txt">Table of n, a(n) for n=1,...,25</
               a>.
%H A091516 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CarolNumber.html">Carol Number</a>
%F A091516 a(k) = 4^A091515(k)-2^(A091515(k)+1)-1 = (2^A091515(k)-1)^2-2. - M. F. 
               Hasler (www.univ-ag.fr/~mhasler), May 15 2008
%t A091516 lst={};Do[p=(2^n-1)^2-2;If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 160}];
               lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
%o A091516 (PARI) c=0;for(n=1,999,ispseudoprime(4^n-2^(n+1)-1)&write("b091516.txt",
               c++," ",4^n-2^(n+1)-1)) - M. F. Hasler (www.univ-ag.fr/~mhasler), 
               May 15 2008
%Y A091516 Cf. A091515.
%Y A091516 Sequence in context: A152988 A009202 A093112 this_sequence A064385 A009260 
               A126635
%Y A091516 Adjacent sequences: A091513 A091514 A091515 this_sequence A091517 A091518 
               A091519
%K A091516 nonn
%O A091516 1,1
%A A091516 Eric Weisstein (eric(AT)weisstein.com), Jan 17, 2004
%E A091516 Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 15, 2004