login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A088054 Factorial primes: primes which are within 1 of a factorial number. 5
2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture: 3 is the intersection of A002981 and A002982.
LINKS
C. Caldwell's The Top Twenty, Factorial Primes.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. - From N. J. A. Sloane, Jun 13 2012
Wikipedia, Factorial prime.
EXAMPLE
3! + 1 = 7; 7! - 1 = 5039.
39916801 is a term because 11! + 1 is prime.
MATHEMATICA
t = {}; Do[ If[PrimeQ[n! - 1], AppendTo[t, n! - 1]]; If[PrimeQ[n! + 1], AppendTo[t, n! + 1]], {n, 50}]; t (* Robert G. Wilson v *)
Union[Select[Range[50]!-1, PrimeQ], Select[Range[50]!+1, PrimeQ]] (Noe)
fp[n_] := Module[{nf=n!}, Select[{nf-1, nf+1}, PrimeQ]]; Flatten[ Table[ fp[i], {i, 50}]] (* Harvey P. Dale, Dec 18 2010 *)
Select[Flatten[#+{-1, 1}&/@(Range[50]!)], PrimeQ] (* Harvey P. Dale, Apr 08 2019 *)
PROG
(Python)
from itertools import count, islice
from sympy import isprime
def A088054_gen(): # generator of terms
f = 1
for k in count(1):
f *= k
if isprime(f-1):
yield f-1
if isprime(f+1):
yield f+1
A088054_list = list(islice(A088054_gen(), 10)) # Chai Wah Wu, Feb 18 2022
CROSSREFS
Union of A055490 and A088332.
Sequence in context: A368805 A262339 A110094 * A249509 A085907 A024777
KEYWORD
easy,nice,nonn
AUTHOR
Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Nov 02 2003
EXTENSIONS
Corrected by Paul Muljadi, Oct 11 2005
More terms from Robert G. Wilson v and T. D. Noe, Oct 12 2005
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)