A288444 Numbers k such that k!6 + 16 is prime, where k!6 is the sextuple factorial number (A085158 ).

1, 3, 7, 9, 11, 13, 15, 21, 23, 35, 37, 39, 47, 49, 59, 111, 117, 163, 287, 311, 601, 635, 855, 895, 2455, 2929, 3369, 7147, 10367, 12311, 13093, 13611, 14431, 17305, 27331

Offset

1,2

Comments

Corresponding primes are: 17, 19, 23, 43, 71, 107, 421, 8521, 21521, 21827591, 49579091, 295540261, 42061737041, 104463111041, ...

a(36) > 50000.

Terms > 49 correspond to probable primes.

Links

Table of n, a(n) for n=1..35.

Henri & Renaud Lifchitz, PRP Records. Search for n!6+16.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

11!6 + 16 = 11*5 + 16 = 71 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[#, 6] + 16] &]
Select[Range[1000], PrimeQ[Times@@Range[#, 1, -6]+16]&] (* The program generates the first 24 terms of the sequence. To generate more, increase the Range constant. *)

Crossrefs

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

Sequence in context: A165631 A245586 A005818 * A085820 A045572 A069254

Adjacent sequences: A288441 A288442 A288443 * A288445 A288446 A288447

Keyword

nonn,more

Author

Robert Price, Jun 09 2017

Status

approved