A127581 Smallest prime of the form k*2^n - 1, for k >= 2.

2, 3, 7, 23, 31, 127, 127, 383, 1279, 3583, 5119, 6143, 8191, 73727, 81919, 131071, 131071, 524287, 524287, 14680063, 14680063, 14680063, 109051903, 109051903, 654311423, 738197503, 738197503, 2147483647, 2147483647, 2147483647

Offset: 0

Author

Artur Jasinski, Jan 19 2007

Keywords

• nonn

Examples

			a(3)=23 because 23 = 3*2^3 - 1 is prime.
a(4)=31 because 31 = 2*2^4 - 1 is prime.
		

Crossrefs

Cf. A007522, A127575-A127582, A127586-A127587.

Programs

Mathematica

a = {}; Do[k = 1; While[ !PrimeQ[k 2^n + 2^n - 1], k++ ]; AppendTo[a, k 2^n + 2^n - 1], {n, 0, 50}]; a

Formula

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

Extensions

Edited by Don Reble, Jun 11 2007