A127582 -id:A127582 - cp's OEIS frontend

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

Artur Jasinski, Jan 19 2007

nonn

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

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

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

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

Edited by Don Reble, Jun 11 2007

A087522 a(0) = 2; for n>=1, a(n) = smallest prime p such that p+1 is divisible by an n-th power > 1.

Original entry on oeis.org

2, 2, 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, 2147483647

Offset: 0

Amarnath Murthy, Sep 11 2003

nonn

Trivially the n-th power under consideration is 2^n for n > 1.

			a(1) = 2 because 3^1|3.
a(2) = 3 because 2^2|4.
a(3) = 7 because 2^3|8.

John Mason, using Robert Israel's data for A127582, Table of n, a(n) for n = 0..3310

A127582 is identical except for a(1).

okdivs(pp1, n) = fordiv(pp1, d, if ((d>1) && ispower(d, n), return (1))); 0
a(n) = {if (n == 0, return (2)); p = 2; while (! okdivs(p+1, n), p = nextprime(p+1)); return (p);} \\ Michel Marcus, Sep 14 2013

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

More terms from Ray Chandler, Sep 14 2003

Edited by N. J. A. Sloane, Jul 03 2008

cp's OEIS Frontend

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

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