A177331 Prime numbers p such that (p*2^k-1)/3 is composite for all even k or all odd k.

557, 743, 919, 1163, 3257, 3301, 4817, 5209, 5581, 6323, 6421, 6983, 7457, 7793

Offset: 1

Author

T. D. Noe, May 08 2010

Keywords

• nonn

Comments

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}.