A106821 Greatest k < n such that 2^n - 2^k -1 is prime or 0 if no such prime exists.

0, 0, 2, 3, 3, 5, 0, 7, 7, 5, 3, 9, 11, 13, 0, 11, 11, 17, 11, 19, 17, 16, 0, 21, 13, 9, 0, 23, 17, 18, 0, 31, 23, 28, 31, 34, 0, 33, 0, 38, 31, 37, 0, 30, 43, 17, 31, 45, 41, 37, 7, 47, 41, 44, 0, 42, 55, 0, 27, 42, 43, 61, 0, 29

Offset

1,3

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

2^3 - 2^2 -1 = 3 prime so a(3)=2
2^4 - 2^3 -1 = 7 prime so a(4)=3
2^5 - 2^3 -1 = 23 prime so a(5)=3
2^6 - 2^5 -1 = 31 prime so a(6)=5

Mathematica

kk[n_]:=Module[{k=n-1, n2=2^n}, While[!PrimeQ[n2-2^k-1]&&k>0, k--]; k]; Array[kk, 70] (* Harvey P. Dale, Mar 09 2012 *)

Prog

(PARI)
for(n=1, 1000, q=1;
  forstep(k=n-1, 0, -1,
    if(isprime(2^n-2^k-1),
      q=0;
      print1(k, ", ");
      break()
     )
  );
  if(q, print1(0, ", "))
) /* Joerg Arndt, Jan 14 2011 */

Crossrefs

Sequence in context: A118963 A127641 A328730 * A065863 A341931 A341701

Adjacent sequences: A106818 A106819 A106820 * A106822 A106823 A106824

Keyword

nonn

Author

Pierre CAMI, May 18 2005

Extensions

Extra numbers to right of data removed from b-file by Andrew Howroyd, Feb 23 2018

Status

approved