The On-Line Encyclopedia of Integer Sequences (OEIS)

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A101747

Numbers n such that ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6 is prime.
(history; published version)

#9 by Wesley Ivan Hurt at Sun Sep 04 11:26:51 EDT 2022

STATUS

editing

approved

#8 by Wesley Ivan Hurt at Sun Sep 04 11:26:34 EDT 2022

COMMENTS

Let S(n) =sum_ Sum_{i=0,..n-1} (i!)^2. Note that 6 divides S(n) for n>1. For prime p=20879, p divides S(p-1). Hence p divides S(n) for all n >= p-1 and all prime values of S(n)/6 are for n < p-1. These n yield provable primes for n <= 93. No other n < 4000.

No other n < 8000. [From __T. D. Noe_, Jul 31 2008]

STATUS

approved

editing

#7 by Bruno Berselli at Thu May 10 05:03:48 EDT 2018

STATUS

proposed

approved

#6 by Michel Marcus at Thu May 10 05:02:46 EDT 2018

STATUS

editing

proposed

#5 by Michel Marcus at Thu May 10 05:02:40 EDT 2018

CROSSREFS

Cf. A061062 (S(n)), A100288 (primes of the form S(n)-1), A100289 (n such that S(n)-1 is prime), A101746 (primes of the for form S(n)/6).

STATUS

approved

editing

Discussion

Thu May 10

05:02

Michel Marcus: typo

#4 by Russ Cox at Fri Mar 30 17:22:34 EDT 2012

COMMENTS

No other n < 8000. [From _T. D. Noe (noe(AT)sspectra.com), _, Jul 31 2008]

AUTHOR

_T. D. Noe (noe(AT)sspectra.com), _, Dec 18 2004

Discussion

Fri Mar 30

17:22

OEIS Server: https://oeis.org/edit/global/120

#3 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

COMMENTS

No other n < 8000. [From T. D. Noe (noe(AT)sspectra.com), Jul 31 2008]

KEYWORD

fini,nonn,new

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

MATHEMATICA

f2=1; s=2; Do[f2=f2*n*n; s=s+f2; If[PrimeQ[s/6], Print[{n, s/6}]], {n, 2, 100}]

KEYWORD

fini,nonn,new

#1 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

NAME

Numbers n such that ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6 is prime.

DATA

3, 4, 5, 6, 7, 19, 40, 56, 93

OFFSET

1,1

COMMENTS

Let S(n)=sum_{i=0,..n-1} (i!)^2. Note that 6 divides S(n) for n>1. For prime p=20879, p divides S(p-1). Hence p divides S(n) for all n >= p-1 and all prime values of S(n)/6 are for n < p-1. These n yield provable primes for n <= 93. No other n < 4000.

MATHEMATICA

f2=1; s=2; Do[f2=f2*n*n; s=s+f2; If[PrimeQ[s/6], Print[{n, s/6}]], {n, 2, 100}]

CROSSREFS

Cf. A061062 (S(n)), A100288 (primes of the form S(n)-1), A100289 (n such that S(n)-1 is prime), A101746 (primes of the for S(n)/6).

KEYWORD

fini,nonn

AUTHOR

T. D. Noe (noe(AT)sspectra.com), Dec 18 2004

STATUS

approved