A100595 Numbers k such that (prime(k)-1)! + prime(k)^9 is prime.

9, 10, 17, 137

Offset

1,1

Comments

There are no more such k up to k=150. Computed in collaboration with Ray Chandler.

a(5) > 1000. - Jinyuan Wang, Apr 11 2020

a(5) > 2700. - Michael S. Branicky, Jul 03 2024

Links

Table of n, a(n) for n=1..4.

Formula

Numbers k such that (prime(k)-1)! + prime(k)^9 is prime, where prime(k) is the k-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 (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)

Prog

(PARI) is(k) = ispseudoprime((prime(k)-1)! + prime(k)^9); \\ Jinyuan Wang, Apr 11 2020

Crossrefs

Cf. A100596, A100598, A100858.

Sequence in context: A191380 A088036 A217935 * A107433 A090570 A131417

Adjacent sequences: A100592 A100593 A100594 * A100596 A100597 A100598

Keyword

nonn,hard,more

Author

Jonathan Vos Post, Nov 30 2004

Status

approved