A103786 a(n) is the minimum k that makes primorial P(n)/A019565(k)+A019565(k) prime, k>=0, n>0.

0, 0, 0, 0, 0, 1, 3, 3, 5, 1, 0, 1, 6, 6, 1, 11, 1, 3, 3, 4, 2, 14, 5, 2, 9, 22, 5, 8, 1, 45, 23, 13, 10, 2, 13, 24, 42, 7, 20, 9, 8, 10, 114, 5, 31, 5, 33, 1, 6, 19, 22, 6, 7, 4, 20, 59, 65, 4, 29, 15, 3, 6, 1, 12, 32, 17, 26, 34, 8, 59, 115, 32, 33, 26, 0, 25, 1, 35, 71, 27, 65, 75, 71, 5

Offset: 1

Author

Lei Zhou, Feb 15 2005

Keywords

• nonn

Comments

This is the k value of A103785. Conjecture: sequence is defined for all n>=1.

Examples

			for n=1, P(1)/A019565(0)+A019565(0)=2/1+1=3 is prime, so a(1)=0;
for n=7, P(7)/A019565(3)+A019565(3)=510510/6+6=85091 is prime, so a(7)=3;
		

Crossrefs

Cf. A019565, A002110, A103785.

Programs

Mathematica

nmax = 2^2048; npd = 2; n = 2; 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[tn]; n = n + 1; npd = npd*Prime[n]]