A103785 Primes of the form A019565(2^n-1-k)+A019565(k) with minimum k.

3, 7, 31, 211, 2311, 15017, 85091, 1616621, 22309297, 3234846617, 200560490131, 3710369067407, 20283350901829, 872184088778017, 307444891294245707, 775932344695001107, 961380175077106319537, 19548063559901161830551

Offset: 1

Author

Lei Zhou, Feb 15 2005

Keywords

• base
• nonn

Comments

This sequence can also be defined as: The Primes of the form primorial P(n)/A019565(k)+A019565(k) with minimum k. Conjecture: sequence is defined for any n>=1.

Examples

			for n=1, A019565(2^1-1-0)+A019565(0)=2+1=3 is prime, so a(1)=3;
for n=6, A019565(2^6-1-1)+A019565(1)=15015+2=15017 is prime, so a(6)=15017;
		

Crossrefs

Cf. A019565, A002110.

Programs

Mathematica

nmax = 2^2048; npd = 1; n = 1; npd = npd*Prime[n]; While[npd < nmax, tn = 0; tt = 1; cp = npd/tt + tt; While[(IntegerQ[cp]) && (! (PrimeQ[cp])), tn = tn + 1; tt = 1; k1 = tn; o = 1; While[k1 > 0, k2 = Mod[k1, 2]; If[k2 == 1, tt = tt*Prime[o]]; k1 = (k1 - k2)/2; o = o + 1]; cp = npd/tt + tt]; Print[cp]; n = n + 1; npd = npd*Prime[n]]