A103515 Primes of the form primorial P(k)*2^n-1 with minimal n, n>=0, k>=2.

5, 29, 419, 2309, 30029, 1021019, 19399379, 892371479, 51757545839, 821495767572479, 14841476269619, 304250263527209, 54873078184468933509119, 2459559130353965639, 521426535635040715679, 15751252788463309939261439

Offset: 1

Author

Lei Zhou, Feb 15 2005

Keywords

• nonn

Comments

Conjecture: sequence is defined for all k>=2

Examples

			P(2)*2^0-1=3*2-1=5 is prime, so a(2)=5;
P(4)*2^1-1=7*5*3*2*2-1=419 is prime, so a(4)=419;
		

Crossrefs

Cf. A002110, A005234, A014545, A018239, A006794, A057704, A057705, A103153, A103154.

Programs

Mathematica

nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[ ! (PrimeQ[cp]), tt = tt*2; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]]