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A135535 Primes of the form 4^n - 3. 5
13, 61, 1021, 4093, 16381, 1048573, 4194301, 16777213, 19807040628566084398385987581, 83076749736557242056487941267521533, 5316911983139663491615228241121378301, 1427247692705959881058285969449495136382746621, 23945242826029513411849172299223580994042798784118781, 118571099379011784113736688648896417641748464297615937576404566024103044751294461, 139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444733 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Involved in the "New Mersenne Prime Conjecture" and in some generalizations of Mersenne primes.

REFERENCES

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

LINKS

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

FORMULA

a(n) = 4^A059266(n) - 3. - Ryan Propper, Feb 26 2008

MATHEMATICA

Do[If[PrimeQ[4^n - 3], Print[4^n - 3]], {n, 100}] (* Robert G. Wilson v, Feb 29 2008 *)

CROSSREFS

Cf. A059266, A057732, A057733.

Sequence in context: A147185 A122885 A257216 * A158870 A145044 A264612

Adjacent sequences:  A135532 A135533 A135534 * A135536 A135537 A135538

KEYWORD

nonn

AUTHOR

Daniele Corradetti (d.corradetti(AT)gmail.com), Feb 21 2008

EXTENSIONS

More terms from R. J. Mathar, Robert G. Wilson v and Ryan Propper, Feb 26 2008

STATUS

approved

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Last modified July 2 04:14 EDT 2022. Contains 354985 sequences. (Running on oeis4.)