|
| |
|
|
A103794
|
|
Smallest number b such that b^Prime(n)-(b-1)^Prime(n) is prime.
|
|
1
| |
|
|
2, 2, 2, 2, 6, 2, 2, 2, 6, 3, 2, 40, 7, 5, 13, 3, 3, 2, 7, 18, 47, 8, 6, 2, 26, 3, 42, 2, 13, 8, 2, 8, 328, 8, 9, 45, 27, 13, 76, 15, 52, 111, 5, 15, 50, 287, 16, 5, 40, 23, 110, 368, 23, 68, 28, 96, 81, 150, 3, 143, 4, 12, 403, 4, 45, 11, 83, 21, 96, 5, 109, 350, 128, 304, 38, 4, 163
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Conjecture: sequence is defined for all positive indices.
For p=prime(n), Eisenstein's irreducibility criterion can be used to show that the polynomial (x+1)^p-x^p is irreducible, which is a necessary (but not sufficient) condition for a(n) to exist. - T. D. Noe (noe(AT)sspectra.com), Dec 05 2005
|
|
|
EXAMPLE
| 2^Prime(1)-1^Prime(1)=3 is prime, so a(1)=2;
2^Prime(5)-1^Prime(5)=2047 has a factor of 23;
...
6^Prime(5)-5^Prime(5)=313968931 is prime, so a(5)=6;
|
|
|
MATHEMATICA
| Do[p=Prime[k]; n=2; nm1=n-1; cp=n^p-nm1^p; While[ !PrimeQ[cp], n=n+1; nm1=n-1; cp=n^p-nm1^p]; Print[n], {k, 1, 200}]
|
|
|
CROSSREFS
| Cf. A103795, A066180, A058013.
Sequence in context: A162489 A079894 A114005 * A073124 A070877 A156717
Adjacent sequences: A103791 A103792 A103793 * A103795 A103796 A103797
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Lei Zhou (lzhou5(AT)emory.edu), Feb 24 2005
|
| |
|
|
