A291349 Numbers k such that k!4 + 2^8 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

1, 7, 11, 31, 57, 73, 97, 105, 209, 245, 403, 545, 917, 953, 1177, 1239, 1283, 1627, 2465, 3701, 4479, 4637, 6349, 7983, 11155, 13595, 15547, 17031, 17609, 24087, 24707, 39773, 40407, 63329

Offset

1,2

Comments

Corresponding primes are: 257, 277, 487, 1267389841, ...

a(35) > 10^5.

Terms > 31 correspond to probable primes.

Links

Table of n, a(n) for n=1..34.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+256.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

11!4 + 2^8 = 11*7*3*1 + 256 = 487 is prime, so 11 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^8] &]

Crossrefs

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

Sequence in context: A027707 A046861 A078917 * A293046 A213176 A236143

Adjacent sequences: A291346 A291347 A291348 * A291350 A291351 A291352

Keyword

nonn,more

Author

Robert Price, Aug 22 2017

Extensions

a(34) from Robert Price, Sep 25 2019

Status

approved