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%I #19 Feb 23 2018 23:30:25
%S 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,
%T 17,18,0,31,23,28,31,34,0,33,0,38,31,37,0,30,43,17,31,45,41,37,7,47,
%U 41,44,0,42,55,0,27,42,43,61,0,29
%N Greatest k < n such that 2^n - 2^k -1 is prime or 0 if no such prime exists.
%H Pierre CAMI, <a href="/A106821/b106821.txt">Table of n, a(n) for n = 1..10000</a>
%e 2^3 - 2^2 -1 = 3 prime so a(3)=2
%e 2^4 - 2^3 -1 = 7 prime so a(4)=3
%e 2^5 - 2^3 -1 = 23 prime so a(5)=3
%e 2^6 - 2^5 -1 = 31 prime so a(6)=5
%t 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 *)
%o (PARI)
%o for(n=1,1000, q=1;
%o forstep(k=n-1,0,-1,
%o if(isprime(2^n-2^k-1),
%o q=0;
%o print1(k,", ");
%o break()
%o )
%o );
%o if(q,print1(0,", "))
%o ) /* Joerg Arndt, Jan 14 2011 */
%K nonn
%O 1,3
%A _Pierre CAMI_, May 18 2005
%E Extra numbers to right of data removed from b-file by _Andrew Howroyd_, Feb 23 2018
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