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A100602 Numbers k such that (prime(k)-1)! + prime(k)^5 is prime. 1
6, 8, 11, 17 (list; graph; refs; listen; history; text; internal format)
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 k-th prime.

EXAMPLE

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

MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+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

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Last modified July 31 17:38 EDT 2021. Contains 346376 sequences. (Running on oeis4.)