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A091516 Carol primes 4^n-2^{n+1}-1. 6
7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447, 274876858367, 4398042316799, 1125899839733759, 18014398241046527, 1298074214633706835075030044377087 (list; graph; refs; listen; history; text; internal format)



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, 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, 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, May 15 2008


lst={}; Do[p=(2^n-1)^2-2; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 160}]; lst [From Vladimir Joseph Stephan Orlovsky, 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, May 15 2008


Cf. A091515.

Sequence in context: A202509 A009202 A093112 * A064385 A009260 A201871

Adjacent sequences:  A091513 A091514 A091515 * A091517 A091518 A091519




Eric W. Weisstein, Jan 17, 2004


Edited by Ray Chandler, Nov 15, 2004



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Last modified December 22 00:41 EST 2014. Contains 252326 sequences.