|
| |
|
|
A100595
|
|
Numbers n such that (prime(n)-1)! + prime(n)^9 is prime.
|
|
0
|
| |
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
There are no more such n up to n=150. Computed in collaboration with Ray Chandler.
|
|
|
LINKS
|
Table of n, a(n) for n=1..4.
|
|
|
FORMULA
|
Numbers n such that (prime(n)-1)! + prime(n)^9 is prime, where prime(n) is the n-th prime.
|
|
|
EXAMPLE
|
a(1) = 9 because (prime(9)-1)! + prime(9)^9 = (23-1)! + 23^9 = 1124000729578760341463 is the smallest prime of this form.
a(2) = 10 because (prime(10)-1)! + prime(10)^9 = (29-1)! + 29^9 = 304888344611713875008649975869 is the 2nd smallest prime of this form.
a(3) = 17, but prime(17) = 59 yields a number that would take 2 full lines of this page; and a(4) = 137 because prime(137) = 773 yields a prime of this form which is 1975 digits long. Note also that 773 = prime(137) = prime(prime(34)).
|
|
|
MATHEMATICA
|
lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+p^9], AppendTo[lst, n]], {n, 12^2}]; lst [From Vladimir Joseph Stephan Orlovsky, Sep 08 2008]
|
|
|
CROSSREFS
|
Cf. A100858.
Sequence in context: A191380 A088036 A217935 * A107433 A090570 A131417
Adjacent sequences: A100592 A100593 A100594 * A100596 A100597 A100598
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Jonathan Vos Post, Nov 30 2004
|
|
|
STATUS
|
approved
|
| |
|
|
