A103154 -id:A103154 - cp's OEIS frontend

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

Lei Zhou, Feb 15 2005

nonn

Conjecture: sequence is defined for all k>=2

			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;

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

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]]

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

Original entry on oeis.org

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

Offset: 1

Lei Zhou, Feb 15 2005

nonn

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

			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;

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

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]]

cp's OEIS Frontend

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

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