OFFSET
1,1
COMMENTS
Involved in the "New Mersenne Prime Conjecture" and in some generalizations of Mersenne primes.
Subsequence of A050415. - Elmo R. Oliveira, Nov 28 2023
REFERENCES
Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (pp. 114-134).
LINKS
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 and 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]
Paul Tannery, Questions 659 et 660, L'Intermédiaire des mathématiciens, Tome II (1895) p. 317.
Eric Weisstein's World of Mathematics, New Mersenne Prime Conjecture
FORMULA
a(n) = 4^A059266(n) - 3. - Ryan Propper, Feb 26 2008
EXAMPLE
16381 is a term because 4^7 - 3 = 16381 is prime.
MATHEMATICA
Do[If[PrimeQ[4^n - 3], Print[4^n - 3]], {n, 100}] (* Robert G. Wilson v, Feb 29 2008 *)
Select[4^Range[200]-3, PrimeQ] (* Harvey P. Dale, Jul 11 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniele Corradetti (d.corradetti(AT)gmail.com), Feb 21 2008
EXTENSIONS
STATUS
approved