A092969 a(1) = 2; for n>1, a(n) = largest prime of the form n!/k + 1, where k < n, or 0 if no such prime exists.

2, 3, 7, 13, 61, 241, 2521, 20161, 72577, 604801, 39916801, 59875201, 3113510401, 17435658241, 186810624001, 10461394944001, 118562476032001, 0, 24329020081766401, 304112751022080001, 12772735542927360001

Offset: 1

Author

Amarnath Murthy, Mar 26 2004

Keywords

• nonn

Comments

Conjecture: There are only finitely many zeros in this sequence. In other words the sequence is identical to A092965 barring a finite set of terms which are zero.

I found zeros for n: 18,51,53,84,95,100,104,106,143,178,180,181,188,202,203,(204). - Robert G. Wilson v, Mar 27 2004

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A092968, A092970.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[n!/k + 1], k++ ]; If[k < n, n!/k + 1, 0]]; Table[ f[n], {n, 22}] (* Robert G. Wilson v, Mar 27 2004 *)

PARI

a(n)=for (i=1,n,if(isprime(n!/i+1),return((n!/i+1))))

Extensions

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 26 2004