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

Author

Artur Jasinski, Jan 19 2007

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

A087522 is identical except for a(1).

Programs

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 *)

Formula

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

Extensions

Edited by Don Reble, Jun 11 2007

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