A127586 Smallest strictly positive integer k such that (k+1)*2^n-1 is prime.

2, 1, 1, 2, 1, 3, 1, 2, 4, 6, 4, 2, 1, 8, 4, 3, 1, 3, 1, 27, 13, 6, 25, 12, 38, 21, 10, 15, 7, 3, 1, 9, 4, 5, 2, 23, 11, 5, 2, 24, 23, 11, 5, 2, 13, 6, 19, 9, 4, 18, 10

Offset: 0

Author

Artur Jasinski, Jan 19 2007

Keywords

• nonn

Comments

The associated prime number list is (k+1)*2^n-1 = 2, 3, 7, 23, 31, 127, 127, 383, 1279, 3583, 5119, 6143, 8191, 73727 for n=0,1,2,3,4,... - R. J. Mathar, Jan 22 2007

Crossrefs

Cf. A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127587.

Programs

Maple

A127586 := proc(n) local k; k:=1 ; while true do if isprime( (k+1)*2^n-1) then RETURN(k) ; fi ; k := k+1 ; od ; end: for n from 0 to 100 do printf("%d, ",A127586(n)) ; od ; # R. J. Mathar, Jan 22 2007

Mathematica

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

Formula

a(n)=A127587(n) if n is not in A000043. - R. J. Mathar, Jan 22 2007

a(n) << 19^n by Xylouris' improvement to Linnik's theorem. - Charles R Greathouse IV, Dec 10 2013