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%I #2 Mar 30 2012 17:22:56
%S 557,743,919,1163,3257,3301,4817,5209,5581,6323,6421,6983,7457,7793
%N Prime numbers p such that (p*2^k-1)/3 is composite for all even k or all odd k.
%C This sequence consists of the primes >3 for which A177330 is zero. k is even when p=1 (mod 6); k is odd when p=5 (mod 6). This problem is similar to that of finding Sierpinski and Riesel numbers (see A076336 and A076337). Compositeness of (p*2^k-1)/3 for all even or all odd k is established by finding a finite set of primes such that at least one member of the set divides each term. For p <= 7797, the set of primes is {3,5,7,13}.
%K nonn
%O 1,1
%A _T. D. Noe_, May 08 2010