

A100604


Numbers k such that (prime(k)1)! + prime(k)^3 is prime.


1




OFFSET

1,1


COMMENTS

k = {2, 3, 4, 28} yields primes p(k) = {3, 5, 7, 107}. There are no more such k up to k=100. Verified by 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)^3 is prime, where prime(k) is the kth prime.


EXAMPLE

a(3) = 4 because (prime(4)1)! + prime(4)^3 = (71)! + 7^3 = 720 + 343 = 1063 is the 3rd prime of this form.


MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[(p1)!+p^3], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)


PROG

(PARI) is(k) = ispseudoprime((prime(k)1)! + prime(k)^3); \\ Jinyuan Wang, Apr 10 2020


CROSSREFS

Cf. A100605, A100858.
Sequence in context: A141565 A098549 A274677 * A062931 A059614 A333074
Adjacent sequences: A100601 A100602 A100603 * A100605 A100606 A100607


KEYWORD

nonn,hard,more


AUTHOR

Jonathan Vos Post, Nov 30 2004


STATUS

approved



