A127587 Smallest nonnegative integer k such that (k+1)*2^n-1 is prime.

2, 1, 0, 0, 1, 0, 1, 0, 4, 6, 4, 2, 1, 0, 4, 3, 1, 0, 1, 0, 13, 6, 25, 12, 38, 21, 10, 15, 7, 3, 1, 0, 4, 5, 2, 23, 11, 5, 2, 24, 23, 11, 5, 2, 13, 6, 19, 9, 4, 18, 10, 20, 19, 9, 4, 2, 31, 15, 7, 3, 1, 0, 11, 5, 2, 66, 62, 42, 62, 39, 19, 9, 4, 14, 11, 5, 2, 54, 46, 29, 14, 29, 14, 63, 31, 15, 7

Offset: 0

Author

Artur Jasinski, Jan 19 2007

Keywords

• nonn

Comments

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586.

Programs

Maple

A127587 := proc(n) local k; k:=0 ; 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, ",A127587(n)) ; od ; # R. J. Mathar, Jan 22 2007

Mathematica

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

Formula

a[A000043(j)]=0 for j=1,2,3,4,... - R. J. Mathar, Jan 22 2007

a(n) = A085427(n) - 1. - Filip Zaludek, Dec 16 2016

Extensions

More terms from R. J. Mathar, Jan 22 2007