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

1,3

Comments

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

a(42) > 10^5.

Terms > 35 correspond to probable primes.

Links

Table of n, a(n) for n=1..41.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+4.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

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

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 *)

Crossrefs

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

Sequence in context: A043060 A029476 A154317 * A323033 A365371 A080705

Adjacent sequences: A291119 A291120 A291121 * A291123 A291124 A291125

Keyword

nonn,more

Author

Robert Price, Aug 17 2017

Extensions

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

Status

approved