A101050 Least k such that prime(n)*2^k-1 is prime, or -1 if no such k exists.

1, 0, 2, 1, 2, 3, 2, 1, 4, 4, 1, 1, 2, 7, 4, 2, 12, 3, 5, 2, 7, 1, 2, 4, 1, 10, 3, 10, 9, 8, 25, 2, 2, 1, 4, 5, 1, 3, 4, 2, 8, 3, 226, 3, 2, 1, 1, 3, 2, 1, 4, 4, 11, 6, 4, 2, 8, 1, 5, 2, 11, 2, 1, 26, 3, 6, 1, 1, 18, 3, 4, 4, 1, 7, 1, 2, 20, 5, 10, 3, 4, 7, 2, 3, 1, 6, 112, 9, 10, 7, 2, 12, 5, 46, 1, 2, 8

Offset: 1

Author

Pierre CAMI, Jan 21 2005

Keywords

• nonn

Comments

Primes p such that p*2^k-1 is composite for all k are called Riesel numbers. The smallest known Riesel number is the prime 509203. Currently, 2293 is the smallest prime whose status is unknown. For a(120), which corresponds to the prime 659, Dave Linton found the least k is 800516. - T. D. Noe, Aug 04 2005

References

• See A046069

Crossrefs

Cf. A046069 (least k such that (2n-1)*2^k-1 is prime).

Programs

Mathematica

Table[p=Prime[n]; k=0; While[ !PrimeQ[ -1+p*2^k], k++ ]; k, {n, 119}] (* T. D. Noe, Aug 04 2005 *)

Extensions

Corrected and extended by T. D. Noe, Aug 04 2005