A093173 -id:A093173 - cp's OEIS frontend

A117141 Primes of the form n!! - 1.

2, 7, 47, 383, 10321919, 51011754393599, 1130138339199322632554990773529330319359999999, 73562883979319395645666688474019139929848516028923903999999999, 4208832729023498248022825567687608993477547383960134557368319999999999

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Apr 21 2006

nonn

			6!! - 1 = 6*4*2 - 1 = 48 - 1 = 47, which is prime.
8!! - 1 = 8*6*4*2 - 1 = 384 - 1 = 383, which is prime.

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 158.

Vincenzo Librandi, Table of n, a(n) for n = 1..15

Cf. A002981, A002982, A006882, A007749, A088332.

Cf. A093173 = primes of the form (2^n * n!) - 1.

SFACT:= proc(n) local i,j,k; for k from 1 by 1 to n do i:=k; j:=k-2; while j >0 do i:=i*j; j:=j-2; od: if isprime(i-1) then print(i-1); fi; od: end: SFACT(100);

lst={};Do[p=n!!-1;If[PrimeQ[p],AppendTo[lst,p]],{n,0,5!,1}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)
Select[Table[n!!-1,{n,1,100}],PrimeQ] (* Vincenzo Librandi, Dec 07 2011 *)

print1(2);for(n=1, 1e3, if(ispseudoprime(t=n!<Charles R Greathouse IV, Jun 16 2011

a(n) = A093173(n-1) for n > 1. - Alexander Adamchuk, Apr 18 2007

a(n) = A006882(A007749(n)) - 1. - Elmo R. Oliveira, Feb 22 2025

A091415 Numbers n such that n!*2^n - 1 is prime.

Original entry on oeis.org

2, 3, 4, 8, 13, 32, 41, 45, 59, 97, 107, 364, 421, 444, 1164, 1663, 3202, 4335, 4841, 13528, 22159, 38095, 50327, 72853

Offset: 1

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004

			a(1)=2 because 2!*2^2 - 1 = 7 is prime
a(2)=3 because 3!*2^3 - 1 = 47 is prime

Ken Davis, Status of Search for Multifactorial Primes.
Ken Davis, Results for n!2-1.

A093173 gives the corresponding primes.

Cf. A007749, A117141, A092075.

For[n=1, n<1000,n++, If[PrimeQ[2^n*n!-1], Print[n]]] (Steinerberger)

f(n)=n!*2^n -1; for (i=1,363,if(isprime(f(i)),print(i)))

a(n) = A007749(n+1)/2. - Alexander Adamchuk, Sep 23 2006

a(12)-a(14) from Stefan Steinerberger, Feb 05 2006
a(15) from Mohammed Bouayoun (Mohammed.Bouayoun(AT)yahoo.fr), Apr 13 2006
More terms from Alexander Adamchuk, Sep 23 2006
Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Terms a(22)..a(24) (using A007749) from Joerg Arndt, Apr 22 2016

A128882 a(n) = n!! - 1.

Original entry on oeis.org

0, 0, 1, 2, 7, 14, 47, 104, 383, 944, 3839, 10394, 46079, 135134, 645119, 2027024, 10321919, 34459424, 185794559, 654729074, 3715891199, 13749310574, 81749606399, 316234143224, 1961990553599, 7905853580624, 51011754393599

Offset: 0

Alexander Adamchuk, Apr 18 2007

nonn

n divides a(n-1) and a(n+1) for n = {1, 2, 8, 11, 16, 19, 23, 31, 32, 43, 64, 67, 71, ...} which include all powers of 2 except 2^2 and some odd primes of the form 4k+3 belonging to A002145.
p^2 divides a(p-1) for odd prime p = 71.
p^2 divides a(p+1) for odd prime p = 23.
a(n) is prime for n = {3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, ...} = A007749; A007749(n) = 2*A091415(n-1) for n > 1. Corresponding primes of the form n!! - 1 are listed in A117141, cf. also A093173.

Eric Weisstein's World of Mathematics, Double Factorial

Cf. A006882, A002145, A117141, A093173, A007749, A091415.

Mathematica
```
Table[ n!! - 1, {n,0,35} ]
```

a(n) = A006882(n) - 1.

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A117141 Primes of the form n!! - 1.

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A091415 Numbers n such that n!*2^n - 1 is prime.

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A128882 a(n) = n!! - 1.

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