OFFSET
1,1
COMMENTS
First four terms are primes. Fifth (1.61585...*10^616), sixth (5.45374...*10^2465), seventh (2.007...*10^39456) and eighth (1.298...*10^157826) are not primes.
Note that a(n) divides 2^a(n)-2 for every n, so if a(n) is composite then a(n) is a Fermat pseudoprime to base 2; cf. A007013. - Thomas Ordowski, Apr 08 2016
A number MM(p) is prime iff M(p) = A000225(p) = 2^p-1 is a Mersenne prime exponent (A000043), which isn't possible unless p itself is also in A000043. Primes of this form are called double Mersenne primes MM(p). For all Mersenne exponents between 7 and 61, factors of MM(p) are known. The next candidate MM(61) is far too large to be merely stored on any existing hard drive (it would require 3*10^17 bytes), but a distributed search for factors of this and other MM(p) is ongoing, see the doublemersenne.org web site. - M. F. Hasler, Mar 05 2020
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..5
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
Luigi Morelli, DoubleMersennes.org
Eric Weisstein's World of Mathematics, Double Mersenne Number
Wikipedia, Double Mersenne number
EXAMPLE
a(3) = 2^(2^5 - 1) - 1 = 2^31 - 1 = 2147483647.
MAPLE
MATHEMATICA
Array[2^(2^Prime[#] - 1) - 1 &, 4] (* Michael De Vlieger, Apr 14 2022 *)
PROG
(PARI) apply( {A077586(n)=2^(2^prime(n)-1)-1}, [1..5]) \\ M. F. Hasler, Mar 05 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Nov 07 2002
STATUS
approved