A291350 Numbers k such that k!4 + 2^9 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

9, 11, 13, 17, 19, 21, 29, 31, 33, 35, 67, 103, 111, 129, 179, 355, 713, 799, 921, 1013, 1389, 1543, 2097, 2287, 3657, 4115, 7031, 10689, 11715, 16401, 16893, 19497, 29737, 35615

Offset

1,1

Comments

Corresponding primes are: 557, 743, 1097, 10457, 66347, 209357, 151413137, ...

a(35) > 10^5.

Terms > 35 correspond to probable primes.

Links

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

Henri & Renaud Lifchitz, PRP Records. Search for n!4+512.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

11!4 + 2^9 = 11*7*3*1 + 512 = 743 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] + 2^9] &]

Crossrefs

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

Sequence in context: A373627 A225557 A120177 * A289697 A104296 A254936

Adjacent sequences: A291347 A291348 A291349 * A291351 A291352 A291353

Keyword

nonn,more

Author

Robert Price, Aug 22 2017

Status

approved