A289696 Numbers k such that k!6 - 18 is prime, where k!6 is the sextuple factorial number (A085158).

11, 13, 23, 25, 35, 85, 89, 91, 103, 127, 161, 265, 295, 385, 605, 719, 913, 1379, 1423, 1481, 1603, 2129, 2603, 3893, 4739, 6461, 7249, 7549, 8149, 10633, 14447, 27463, 30323, 33991, 35821, 42221, 46525, 59057

Offset

1,1

Comments

Corresponding primes are: 37, 73, 21487, 43207, 21827557, 11510631741140058401857, ...

a(39) > 10^5.

Terms > 35 correspond to probable primes.

Links

Table of n, a(n) for n=1..38.

Henri & Renaud Lifchitz, PRP Records. Search for n!6-18.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

13!6 - 18 = 13*7 - 18 = 73 is prime, so 13 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[9, 50000], PrimeQ[MultiFactorial[#, 6] - 18] &]
Select[Range[11, 60000], PrimeQ[Times@@Range[#, 1, -6]-18]&] (* Harvey P. Dale, Aug 10 2019 *)

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994.

Sequence in context: A160373 A091998 A208296 * A365313 A023232 A075519

Adjacent sequences: A289693 A289694 A289695 * A289697 A289698 A289699

Keyword

nonn,more

Author

Robert Price, Jul 09 2017

Extensions

a(38) from Robert Price, Aug 03 2018

Status

approved