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

1,1

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.

Links

Table of n, a(n) for n=1..18.

Example

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;

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]]

Crossrefs

Cf. A019565, A002110.

Sequence in context: A051342 A002585 A365021 * A289127 A289125 A083772

Adjacent sequences: A103782 A103783 A103784 * A103786 A103787 A103788

Keyword

base,nonn

Author

Lei Zhou, Feb 15 2005

Status

approved