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A091516
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Carol primes 4^n-2^{n+1}-1.
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6
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7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447, 274876858367, 4398042316799, 1125899839733759, 18014398241046527, 1298074214633706835075030044377087
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
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LINKS
| M. F. Hasler, Table of n, a(n) for n=1,...,25.
Eric Weisstein's World of Mathematics, Carol Number
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FORMULA
| 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
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MATHEMATICA
| 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]
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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 (www.univ-ag.fr/~mhasler), May 15 2008
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CROSSREFS
| Cf. A091515.
Sequence in context: A202509 A009202 A093112 * A064385 A009260 A201871
Adjacent sequences: A091513 A091514 A091515 * A091517 A091518 A091519
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Jan 17, 2004
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EXTENSIONS
| Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 15, 2004
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