login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A100603 Numbers k such that (prime(k)-1)! + prime(k)^4 is prime. 0
1, 2, 4, 67, 212, 1615 (list; graph; refs; listen; history; text; internal format)
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 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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 25 03:09 EDT 2021. Contains 345449 sequences. (Running on oeis4.)