1,1

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

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

M. F. Hasler, Table of n, a(n) for n=1,...,25.

Eric Weisstein's World of Mathematics, Carol Number

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

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]

(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

Cf. A091515.

Sequence in context: A152988 A009202 A093112 this_sequence A064385 A009260 A126635

Adjacent sequences: A091513 A091514 A091515 this_sequence A091517 A091518 A091519

nonn

Eric Weisstein (eric(AT)weisstein.com), Jan 17, 2004

Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 15, 2004