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A100604 Numbers k such that (prime(k)-1)! + prime(k)^3 is prime. 1

%I

%S 2,3,4,28

%N Numbers k such that (prime(k)-1)! + prime(k)^3 is prime.

%C 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_.

%C a(5) > 600. - _Jinyuan Wang_, Apr 10 2020

%F Numbers k such that (prime(k)-1)! + prime(k)^3 is prime, where prime(k) is the k-th prime.

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

%t 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 *)

%o (PARI) is(k) = ispseudoprime((prime(k)-1)! + prime(k)^3); \\ _Jinyuan Wang_, Apr 10 2020

%Y Cf. A100605, A100858.

%K nonn,hard,more

%O 1,1

%A _Jonathan Vos Post_, Nov 30 2004

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Last modified August 1 18:37 EDT 2021. Contains 346402 sequences. (Running on oeis4.)