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A100603
Numbers k such that (prime(k)-1)! + prime(k)^4 is prime.
0
1, 2, 4, 67, 212, 1615
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
FORMULA
Numbers k such that (prime(k)-1)! + prime(k)^4 is prime, where prime(k) is the k-th prime.
EXAMPLE
a(3) = 4 because (prime(4)-1)! + prime(4)^4 = (7-1)! + 7^4 = 720 + 2401 = 3121 is the 3rd prime of this form.
MATHEMATICA
lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+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((p-1)! + p^4) \\ Iain Fox, Mar 05 2018
CROSSREFS
Cf. A100858.
Sequence in context: A279969 A361228 A018364 * A374235 A362456 A301818
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