A135726 -id:A135726 - cp's OEIS frontend

A084438 Positive integers k such that k!!! - 1 = A007661(k) - 1 is prime.

3, 4, 6, 8, 20, 26, 36, 50, 60, 114, 135, 138, 248, 315, 351, 429, 642, 5505, 8793, 12086, 13580, 23109, 34626, 34706, 56282, 57675, 58298

Offset: 1

Hugo Pfoertner, Jun 25 2003

The search for multifactorial primes started by Ray Ballinger is now continued by a team of volunteers on the website of Ken Davis (see link).

			a(4) = 8 since 8!!! - 1 = 8*5*2 - 1 = 79 is the 4th prime of that form.
26!!! - 1 = 2504902399 is prime.

Ken Davis, Status of Search for Multifactorial Primes.
Ken Davis, Results for n!3-1.
Shyam Sunder Gupta, Fascinating Factorials, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 16, 411-442.
ProthSearch.net (on web.archive.org), n3minus.txt.

Cf. A007661, A135726, A037082, A037083.

multiFactorial[n_, k_] := If[n < 1, 1, n * multiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[multiFactorial[#, 3] - 1] & ] (* Robert Price, Apr 19 2019 *)
Select[Range[650], PrimeQ[Times @@ Range[#, 1, -3] - 1] &] (* The program generates the first 17 terms of the sequence. To generate more, change the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, May 22 2021 *)

A007661(n) = prod(i=1,(n-1)\3,n-=3,n+!n)
for(n=1,999,if(isprime(A007661(n)-1),print1(n","))) \\ M. F. Hasler, Nov 26 2007

Missing 26 inserted by M. F. Hasler, Nov 26 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Edited by N. J. A. Sloane, Feb 11 2009 at the suggestion of M. F. Hasler

A274386 Triple factorial primes: primes which are within 1 of a triple factorial number.

Original entry on oeis.org

2, 3, 5, 11, 17, 19, 29, 79, 163, 281, 881, 209441, 4188799, 264539521, 2504902399, 72642169601, 254561089305599, 9927882482918401, 26582634158080001, 13106744139423334399999, 141383412854531380076544001, 427380210218181008588800001

Offset: 1

Arkadiusz Wesolowski, Jun 19 2016

nonn

Union of A037082 and A135726.

			a(7) = 29 = 4*7 + 1 = 7!!! + 1 is the 7th prime of that form.
a(8) = 79 = 2*5*8 - 1 = 8!!! - 1 is the 8th prime of that form.

Index entries for sequences related to factorial numbers

Cf. A007661, A037082, A037083, A084438, A135726.

r:=59; I:=[1, 1, 2]; lst1:=[n le 3 select I[n] else (n-1)*Self(n-3): n in [1..r]]; lst2:=[]; for c in [1..r] do a:=lst1[c]; for s in [-1..1 by 2] do p:=a+s; if IsPrime(p) and not p in lst2 then Append(~lst2, p); end if; end for; end for; lst2;

Select[Union@ Flatten@ Map[{# - 1, # + 1} &, Table[With[{q = Quotient[n + 2, 3]}, 3^q q! Binomial[n/3, q]], {n, 0, 58}]], PrimeQ] (* Michael De Vlieger, Jun 21 2016, after Jan Mangaldan at A007661 *)
Select[Union[Flatten[#+{1,-1}&/@Table[Times@@Range[n,1,-3],{n,100}]]],PrimeQ] (* Harvey P. Dale, Sep 05 2022 *)

cp's OEIS Frontend

A084438 Positive integers k such that k!!! - 1 = A007661(k) - 1 is prime.

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