A103784 Minimal n that makes primorial P(k)*n-1 prime, k>=2, n>0.

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

Offset: 2

Author

Lei Zhou, Feb 15 2005

Keywords

• nonn

Comments

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

Examples

			P(2)*1-1=5 is prime, so a(2)=1;
P(9)*3-1=669278609 is prime, so a(9)=3;
		

Crossrefs

Cf. A002110, A103515, A103783.

Programs

Mathematica

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]]