|
| |
|
|
A103786
|
|
a(n) is the minimum k that makes primorial P(n)/A019565(k)+A019565(k) prime, k>=0, n>0.
|
|
2
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,7
|
|
|
COMMENTS
| This is the k value of A103785. Conjecture: sequence is defined for all n>=1.
|
|
|
EXAMPLE
| 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;
|
|
|
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]]
|
|
|
CROSSREFS
| Cf. A019565, A002110, A103785.
Sequence in context: A011445 A197137 A133456 * A067462 A021753 A062563
Adjacent sequences: A103783 A103784 A103785 * A103787 A103788 A103789
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Lei Zhou (lzhou5(AT)emory.edu), Feb 15 2005
|
| |
|
|
