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A100604 Numbers k such that (prime(k)-1)! + prime(k)^3 is prime. 1
2, 3, 4, 28 (list; graph; refs; listen; history; text; internal format)
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 k-th prime.

EXAMPLE

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

MATHEMATICA

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

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Last modified June 19 02:43 EDT 2021. Contains 345125 sequences. (Running on oeis4.)