%I #4 Mar 31 2012 10:23:47

%S 1,1,2,1,1,2,2,3,6,3,2,1,18,3,7,13,11,24,2,13,2,16,1,4,29,6,18,4,2,11,

%T 14,13,38,13,14,9,17,12,13,10,31,19,5,58,5,15,22,18,8,5,11,27,24,13,

%U 10,11,3,36,18,19,13,16,12,3,1,53,1,11,19,15,81,14,28,7,5,57,40,40,46,6,10

%N Minimal n that makes primorial P(k)*n-1 prime, k>=2, n>0.

%C Minimal n of sequence A103783. Weak conjecture: sequence is defined for all k>=2; strong conjecture: a(k)<=(prime(k))^2;

%e P(2)*1-1=5 is prime, so a(2)=1;

%e P(9)*3-1=669278609 is prime, so a(9)=3;

%t 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]; If[tt >= (Prime[n])^2, cp = -cp; tn1 = -tt, tn1 = tt]; Print[tn1]; n = n + 1; npd = npd*Prime[n]]

%Y Cf. A002110, A103515, A103783.

%K nonn

%O 2,3

%A _Lei Zhou_, Feb 15 2005