A127582 a(n) = the smallest prime number of the form k*2^n - 1, for k >= 1.

2, 3, 3, 7, 31, 31, 127, 127, 1279, 3583, 5119, 6143, 8191, 8191, 81919, 131071, 131071, 131071, 524287, 524287, 14680063, 14680063, 109051903, 109051903, 654311423, 738197503, 738197503, 2147483647, 2147483647, 2147483647

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..3310

Formula

a(n) << 37^n by Xylouris's improvement to Linnik's theorem. - Charles R Greathouse IV, Dec 10 2013

Example

a(0)=2 because 2 = 3*2^0 - 1 is prime.
a(1)=3 because 3 = 2*2^1 - 1 is prime.
a(2)=3 because 3 = 1*2^2 - 1 is prime.
a(3)=7 because 7 = 1*2^3 - 1 is prime.
a(4)=31 because 31 = 2*2^4 - 1 is prime.

Maple

p:= 2: A[0]:= 2:
for n from 1 to 100 do
  if p+1 mod 2^n = 0 then A[n]:= p
  else
    p:=p+2^(n-1);
    while not isprime(p) do p:= p+2^n od:
    A[n]:= p;
  fi
od:
seq(A[i], i=0..100); # Robert Israel, Jan 13 2017

Mathematica

a = {}; Do[k = 0; While[ !PrimeQ[k 2^n + 2^n - 1], k++ ]; AppendTo[a, k 2^n + 2^n - 1], {n, 0, 50}]; a (* Artur Jasinski, Jan 19 2007 *)

Crossrefs

Cf. A007522, A127575-A127581, A127583-A127587.

A087522 is identical except for a(1).

Sequence in context: A176022 A316275 A113031 * A157144 A096714 A078035

Adjacent sequences: A127579 A127580 A127581 * A127583 A127584 A127585

Keyword

nonn

Author

Artur Jasinski, Jan 19 2007

Extensions

Edited by Don Reble, Jun 11 2007

Further edited by N. J. A. Sloane, Jul 03 2008

Status

approved