This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A103783 #8 Jul 03 2012 16:01:28 %S A103783 5,29,419,2309,30029,1021019,19399379,669278609,38818159379, %T A103783 601681470389,14841476269619,304250263527209,235489703970060539, %U A103783 1844669347765474229,228124109340330313109,24995884552004764307909 %N A103783 Primes of the form primorial P(k)*n-1 with minimal n, n>0, k>=2. %C A103783 Weak conjecture: sequence is defined for all k>=2; strong conjecture: n<(prime(k))^2; %C A103783 Smallest prime p such that the prime factorization of p+1 contains the first n+1 primes. - _R. J. Mathar_, Jul 03 2012 %e A103783 P(2)*1-1=5 is prime, so a(2)=5; %e A103783 P(9)*3-1=669278609 is prime, so a(9)=669278609; %t A103783 nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[(tt <= (Prime[n])^2) && (! (PrimeQ[cp])), tt = tt + 1; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]] %Y A103783 Cf. A002110, A103515, A103782, A073917, A214089. %K A103783 nonn %O A103783 1,1 %A A103783 _Lei Zhou_, Feb 15 2005