A135726 Primes of the form k!!! - 1 = A007661(k) - 1, k > 0.

2, 3, 17, 79, 4188799, 2504902399, 254561089305599, 13106744139423334399999, 8483004771271882804592639999, 706526001186582385898210420541078864497278132689882316799999999, 353401447088718405944982176443380974931403135679741865504466985287679999999999

Offset: 1

Author

M. F. Hasler, Nov 26 2007

Keywords

• nonn

Comments

Sequence A084438 gives the easier-to-read n-values.

All terms greater than a(3) seem to end in the digit 9, or many 9 digits. a(17) ends with 51 9 digits. - Harvey P. Dale, Nov 28 2019

Examples

			a(4) = 79 = 8*5*2 - 1 = 8!!! - 1 is the 4th prime of that form.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..17
• Ken Davis, Status of Search for Multifactorial Primes.
• Ken Davis, Results for n!3-1.
• ProthSearch.net (on web.archive.org), n3minus.txt.

Crossrefs

Cf. A007661, A037082, A037083, A084438.

Programs

Mathematica

Select[Table[Times@@Range[n,1,-3],{n,150}]-1,PrimeQ] (* Harvey P. Dale, Nov 28 2019 *)

PARI

A007661(n) = prod(i=1,(n-1)\3,n-=3,n+!n)
for(n=1,999,if(isprime(A007661(n)-1),print1(A007661(n)-1,",")))

Formula

a(n) = A007661(A084438(n)) - 1. - Elmo R. Oliveira, Feb 25 2025