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A135535
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Primes of the form 4^n - 3.
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5
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13, 61, 1021, 4093, 16381, 1048573, 4194301, 16777213, 19807040628566084398385987581, 83076749736557242056487941267521533, 5316911983139663491615228241121378301, 1427247692705959881058285969449495136382746621, 23945242826029513411849172299223580994042798784118781, 118571099379011784113736688648896417641748464297615937576404566024103044751294461, 139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444733
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OFFSET
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1,1
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COMMENTS
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Involved in the "New Mersenne Prime Conjecture" and in some generalizations of Mersenne primes.
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REFERENCES
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Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (p.114-134) [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009]
Tanner, L'intermediaire des math., 2 (1895), 317
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LINKS
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Table of n, a(n) for n=1..15.
P. T. Bateman, J. L. Selfridge and S. S. Wagstaff, Jr., The New Mersenne Conjecture, Amer. Math. Monthly 96, 125-128, 1989.
D. Minoli and Robert Bear, Hyperperfect Numbers, Pi Mu Epsilon Journal, Fall 1975, pp. 153-157. [Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009]
Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing. [Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009]
Wolfram MathWorld, New Mersenne Prime Conjecture
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FORMULA
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a(n) = 4^A059266(n) - 3. - Ryan Propper, Feb 26 2008
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MATHEMATICA
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Do[If[PrimeQ[4^n - 3], Print[4^n - 3]], {n, 100}] (* Robert G. Wilson v, Feb 29 2008 *)
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CROSSREFS
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Cf. A059266, A057732, A057733.
Sequence in context: A147185 A122885 A257216 * A158870 A145044 A264612
Adjacent sequences: A135532 A135533 A135534 * A135536 A135537 A135538
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KEYWORD
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nonn
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AUTHOR
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Daniele Corradetti (d.corradetti(AT)gmail.com), Feb 21 2008
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EXTENSIONS
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More terms from R. J. Mathar, Robert G. Wilson v and Ryan Propper, Feb 26 2008
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STATUS
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approved
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