A291122 Numbers k such that k!4 + 2^2 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

0, 1, 3, 15, 17, 19, 23, 25, 27, 29, 35, 49, 63, 79, 87, 105, 139, 319, 339, 409, 441, 477, 1023, 1107, 1517, 1557, 1625, 4215, 5297, 6291, 6499, 7357, 11639, 12963, 13989, 15825, 19993, 20535, 35391, 58483, 69247

Offset: 1

Author

Robert Price, Aug 17 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 5, 5, 7, 3469, 9949, 65839, 1514209, 5221129, 40883539, ...

a(42) > 10^5.

Terms > 35 correspond to probable primes.

Examples

			15!4 + 2^2 = 15*11*7*3*1 + 4 = 3469 is prime, so 15 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!4+4.
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^2] &]
Select[Range[0,4300],PrimeQ[Times@@Range[#,1,-4]+4]&] (* The program generates the first 28 terms of the sequence. *) (* Harvey P. Dale, Sep 16 2024 *)

Extensions

a(40)-a(41) from Robert Price, Sep 25 2019