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A077586 a(n) = 2^(2^prime(n) - 1) - 1. 7
7, 127, 2147483647, 170141183460469231731687303715884105727 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..4.

Eric Weisstein's World of Mathematics, Double Mersenne Number

FORMULA

a(n) = A077585(A000040(n)) = A000225(A001348(n)).

EXAMPLE

a(3) = 2^(2^5 - 1) - 1 = 2^31 - 1 = 2147483647.

MAPLE

A077586 := n -> 2^(2^ithprime(n)-1)-1; A077586(n) $ n=1..5; # M. F. Hasler, Mar 05 2020

MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[x=2^(2^p-1)-1], Print[x]; AppendTo[lst, n]], {n, 10^9}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

PROG

(PARI) apply( {A077586(n)=2^(2^prime(n)-1)-1}, [1..5]) \\ M. F. Hasler, Mar 05 2020

CROSSREFS

Cf. A077585 (double Mersenne numbers), A000225 (Mersenne numbers), A001348 (ditto with prime indices), A000040 (primes).

Sequence in context: A261487 A134722 A053713 * A277634 A309130 A263686

Adjacent sequences:  A077583 A077584 A077585 * A077587 A077588 A077589

KEYWORD

nonn

AUTHOR

Henry Bottomley, Nov 07 2002

STATUS

approved

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Last modified July 1 23:45 EDT 2020. Contains 335389 sequences. (Running on oeis4.)