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 A091516 Primes of the form 4^n - 2^(n+1) - 1. 8
 7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447, 274876858367, 4398042316799, 1125899839733759, 18014398241046527, 1298074214633706835075030044377087 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Cletus Emmanuel calls these "Carol primes". 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- and 17-digit primes, there is a 34-digit prime, then a 78-digit prime and some others up to 105 digits, then some 200- to 250-digit primes, then approximately 500 digits...). - M. F. Hasler, May 15 2008 LINKS M. F. Hasler, Table of n, a(n) for n = 1..25. Eric Weisstein's World of Mathematics, Near-Square Prime FORMULA a(k) = 4^A091515(k) - 2^(A091515(k) + 1) - 1 = (2^A091515(k) - 1)^2 - 2. - M. F. Hasler, May 15 2008 MATHEMATICA lst={}; Do[p=(2^n-1)^2-2; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 160}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *) PROG (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 CROSSREFS Cf. A091515. Sequence in context: A202509 A009202 A093112 * A064385 A269520 A009260 Adjacent sequences:  A091513 A091514 A091515 * A091517 A091518 A091519 KEYWORD nonn AUTHOR Eric W. Weisstein, Jan 17 2004 EXTENSIONS Edited by Ray Chandler, Nov 15 2004 STATUS approved

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Last modified August 14 19:42 EDT 2020. Contains 336483 sequences. (Running on oeis4.)