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


%S 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,

%T 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,

%U 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

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

%C 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

%D See A046069

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

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

%K nonn

%O 1,3

%A _Pierre CAMI_, Jan 21 2005

%E Corrected and extended by _T. D. Noe_, Aug 04 2005

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Last modified January 22 02:05 EST 2020. Contains 331133 sequences. (Running on oeis4.)