A305076 Numbers k such that prime(k)^k - primorial(k - 1) is prime.

2, 4, 5, 8, 9, 15, 29, 213, 666, 1360, 3932, 7916

Offset

1,1

Comments

Numbers k such that A304917(k) is prime.

a(12) > 4000 if it exists.

Links

Table of n, a(n) for n=1..12.

Example

n = 1 gives 2 - 1 = 1. n=2 gives 3^2 - 2 = 7, so 2 is the first term.

Maple

N:=2000:
  for X from 1 to N do
Z:=mul(ithprime(i), i=1..(X-1));
Y:=(ithprime(X)^X - Z);
if isprime(Y) then print(X);
end if
end do:

Mathematica

Select[Range@ 700, PrimeQ[Prime[#]^# - Product[Prime@ i, {i, # - 1}]] &] (* Michael De Vlieger, Jul 19 2018 *)

Prog

(PARI) isok(k) = isprime(prime(k)^k - prod(j=1, k-1, prime(j))); \\ Michel Marcus, Jun 09 2018

Crossrefs

Cf. A062457, A002110, A304917.

Sequence in context: A271392 A195364 A279793 * A332223 A269361 A200947

Adjacent sequences: A305073 A305074 A305075 * A305077 A305078 A305079

Keyword

nonn,more

Author

David James Sycamore, May 24 2018

Extensions

a(12) from Michael S. Branicky, Jun 11 2024

Status

approved