A291343 Numbers k such that k!4 + 2^3 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

3, 5, 7, 9, 11, 13, 19, 23, 25, 33, 39, 41, 63, 67, 71, 85, 87, 91, 133, 171, 243, 291, 1239, 1543, 1879, 2169, 2421, 3149, 3323, 3377, 3501, 3529, 5433, 5599, 7299, 11227, 11275, 13939, 27147, 32435, 86455, 92105

Offset

1,1

Comments

Corresponding primes are: 11, 13, 29, 53, 239, 593, 65843, 1514213, 5221133, ...

a(43) > 10^5.

Terms > 33 correspond to probable primes.

Links

Table of n, a(n) for n=1..42.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+8.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

13!4 + 2^3 = 13*9*5*1 + 8 = 593 is prime, so 13 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^3] &]
Select[Range[100000], PrimeQ[Times@@Range[#, 1, -4]+8]&] (* Harvey P. Dale, Oct 29 2022 *)

Crossrefs

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

Sequence in context: A309361 A133854 A239008 * A030155 A143448 A226484

Adjacent sequences: A291340 A291341 A291342 * A291344 A291345 A291346

Keyword

nonn,more

Author

Robert Price, Aug 22 2017

Extensions

a(41)-a(42) from Robert Price, Sep 25 2019

Status

approved