

A100602


Numbers k such that (prime(k)1)! + prime(k)^5 is prime.


1




OFFSET

1,1


COMMENTS

k = {6, 8, 11, 17} yields primes p(k) = {13, 19, 31, 59}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.
a(5) > 600.  Jinyuan Wang, Apr 10 2020


LINKS

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


FORMULA

Numbers k such that (prime(k)1)! + prime(k)^5 is prime, where prime(k) is the kth prime.


EXAMPLE

a(1) = 6 because (prime(6)1)! + prime(6)^5 = (131)! + 13^5 = 479372893 is the first prime of this form.


MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[(p1)!+p^5], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)


PROG

(PARI) is(k) = ispseudoprime((prime(k)1)! + prime(k)^5); \\ Jinyuan Wang, Apr 10 2020


CROSSREFS

Cf. A100600, A100858.
Sequence in context: A183208 A048586 A080824 * A183979 A222175 A315856
Adjacent sequences: A100599 A100600 A100601 * A100603 A100604 A100605


KEYWORD

nonn,hard,more


AUTHOR

Jonathan Vos Post, Nov 30 2004


STATUS

approved



