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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 (list; graph; refs; listen; history; text; internal format)
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 BC--2012) 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[{nf-1, 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

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

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Last modified September 23 20:25 EDT 2014. Contains 247189 sequences.