

A100603


Numbers k such that (prime(k)1)! + prime(k)^4 is prime.


0




OFFSET

1,2


COMMENTS

k = {1, 2, 4, 67} yields primes p(k) = {2, 3, 7, 331}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.
Terms a(5) and greater are only probable primes.  Iain Fox, Mar 05 2018


LINKS

Table of n, a(n) for n=1..6.
J. V. Post, Math Pages.


FORMULA

Numbers k such that (prime(k)1)! + prime(k)^4 is prime, where prime(k) is the kth prime.


EXAMPLE

a(3) = 4 because (prime(4)1)! + prime(4)^4 = (71)! + 7^4 = 720 + 2401 = 3121 is the 3rd prime of this form.


MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[(p1)!+p^4], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)


PROG

(PARI) is(k) = my(p=prime(k)); ispseudoprime((p1)! + p^4) \\ Iain Fox, Mar 05 2018


CROSSREFS

Cf. A100858.
Sequence in context: A219735 A279969 A018364 * A301818 A054920 A062061
Adjacent sequences: A100600 A100601 A100602 * A100604 A100605 A100606


KEYWORD

nonn,more


AUTHOR

Jonathan Vos Post, Nov 30 2004


EXTENSIONS

a(5) from Iain Fox, Mar 05 2018
a(6) from Iain Fox, Mar 11 2018


STATUS

approved



