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A127582
a(n) = the smallest prime number of the form k*2^n - 1, for k >= 1.
3
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
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
A087522 is identical except for a(1).
Sequence in context: A176022 A316275 A113031 * A157144 A096714 A078035
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