A103788 a(n) = number of ks that make primorial P(n)/A019565(k)-A019565(k) prime.

0, 1, 3, 6, 13, 28, 39, 78, 138, 207, 437, 865, 1423, 2750, 4904, 8861, 16201, 33346, 58534, 111878, 208914, 397522

Offset: 1

Author

Lei Zhou, Feb 16 2005

Keywords

• hard
• nonn

Examples

			P(2)/A(0)-A(0)=6-1=5 is prime, so a(2)=1;
P(4)/A(k)-A(k): 210/2-2=103; 210/3-3=67; 210/6-6=29; 210/5-5=37; 210/10-10=11; 210/7-7=23; so a(4)=6;
		

Crossrefs

Cf. A019565, A002110, A103785, A103786, A103787.

Programs

Mathematica

npd = 1; Do[npd = npd*Prime[n]; tn = 0; tt = 1; cp = npd/tt - tt; ct = 0; While[IntegerQ[cp], If[(cp > 0) && PrimeQ[cp], ct = ct + 1]; 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[ct], {n, 1, 22}]