

A088054


Factorial primes: primes which are within 1 of a factorial number.


3



2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999
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OFFSET

1,1


COMMENTS

Conjecture: 3 is the intersection of A002981 and A002982.


LINKS

Table of n, a(n) for n=1..14.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012  From N. J. A. Sloane, Jun 13 2012
Wikipedia, Factorial prime.
C. Caldwell's The Top Twenty, Factorial Primes.


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[{nf1, nf+1}, PrimeQ]]; Flatten[Table[fp[i], {i, 50}]] [From Harvey P. Dale, Dec. 18, 2010]


CROSSREFS

Cf. A000142, A002981, A002982.
Union of A055490 and A088332.
Sequence in context: A062088 A070029 A110094 * A085907 A024777 A002957
Adjacent sequences: A088051 A088052 A088053 * A088055 A088056 A088057


KEYWORD

easy,nice,nonn,changed


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



