A103513 Primes of the form primorial(P(k))/2-2^n with minimal n, n>=0, k>=2.

2, 13, 103, 1153, 15013, 255253, 4849843, 111546433, 3234846607, 100280245063, 3710369067401, 152125131763603, 6541380632280583, 307444891294245701, 16294579238595022363, 961380175077106319471, 58644190679703485491571

Offset: 1

Author

Lei Zhou, Feb 15 2005

Keywords

• nonn

Comments

The Mathematica Program does not produce a(2). Conjecture: sequence is defined for all k>=2.

Examples

			P(2)/2=3, 3-2^0=2 is prime, so a(2)=2;
P(5)/2=1155, 1155-2^1=1153 is prime, so a(5)=1153;
		

Crossrefs

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

Programs

Mathematica

nmax = 2^8192; npd = 1; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 2; cp = npd - tt; While[(cp > 1) && (! (PrimeQ[cp])), tt = tt*2; cp = npd - tt]; If[cp < 2, Print["*"], Print[cp]]; n = n + 1; npd = npd*Prime[n]]