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A127582 a(n) = the smallest prime number of the form k*2^n - 1, for k >= 1. 3

%I

%S 2,3,3,7,31,31,127,127,1279,3583,5119,6143,8191,8191,81919,131071,

%T 131071,131071,524287,524287,14680063,14680063,109051903,109051903,

%U 654311423,738197503,738197503,2147483647,2147483647,2147483647

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

%H Robert Israel, <a href="/A127582/b127582.txt">Table of n, a(n) for n = 0..3310</a>

%F a(n) << 37^n by Xylouris's improvement to Linnik's theorem. - _Charles R Greathouse IV_, Dec 10 2013

%e a(0)=2 because 2 = 3*2^0 - 1 is prime.

%e a(1)=3 because 3 = 2*2^1 - 1 is prime.

%e a(2)=3 because 3 = 1*2^2 - 1 is prime.

%e a(3)=7 because 7 = 1*2^3 - 1 is prime.

%e a(4)=31 because 31 = 2*2^4 - 1 is prime.

%p p:= 2: A[0]:= 2:

%p for n from 1 to 100 do

%p if p+1 mod 2^n = 0 then A[n]:= p

%p else

%p p:=p+2^(n-1);

%p while not isprime(p) do p:= p+2^n od:

%p A[n]:= p;

%p fi

%p od:

%p seq(A[i],i=0..100); # _Robert Israel_, Jan 13 2017

%t 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 *)

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

%Y A087522 is identical except for a(1).

%K nonn

%O 0,1

%A _Artur Jasinski_, Jan 19 2007

%E Edited by _Don Reble_, Jun 11 2007

%E Further edited by _N. J. A. Sloane_, Jul 03 2008

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Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)