A283553 Numbers k such that k![4] + 2 is prime, where k![4] = A007662(k) = quadruple factorial.

0, 1, 3, 5, 7, 9, 11, 13, 15, 19, 27, 29, 31, 43, 53, 75, 143, 169, 185, 235, 259, 363, 365, 457, 493, 573, 777, 1273, 1275, 1865, 3621, 4523, 5291, 5845, 7185, 10183, 12845, 15057, 16281, 17945, 18771, 22479, 27235, 28089, 31557, 39163, 45709, 46329, 52211, 77779

Offset: 1

Author

Robert Price, Mar 10 2017

Keywords

• nonn

Comments

a(51) > 10^5.

The first 10 primes associated with this sequence: 3, 3, 5, 7, 23, 47, 233, 587, 3467, 65837.

Links

• C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75
• Ken Davis, Status of Search for Multifactorial Primes.

Crossrefs

Cf. A076185, A085158, A094144, A204657.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2] &]
Select[Range[0,78000],PrimeQ[Times@@Range[#,1,-4]+2]&] (* Harvey P. Dale, Aug 16 2023 *)

Extensions

a(49)-a(50) from Robert Price, Aug 12 2017