A006990 Largest prime <= n!.

2, 5, 23, 113, 719, 5039, 40289, 362867, 3628789, 39916787, 479001599, 6227020777, 87178291199, 1307674367953, 20922789887947, 355687428095941, 6402373705727959, 121645100408831899, 2432902008176639969, 51090942171709439969, 1124000727777607679927

Offset: 2

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn

Comments

Conjecture: For n >= 2, n! - a(n) is 1 or a prime, see A033933. - Amarnath Murthy, Mar 19 2002

a(n) is the largest prime divisor of (n!)! of the sequence A000197. - Stanislav Sykora, Jul 14 2014

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Donovan Johnson, Table of n, a(n) for n = 2..400
• R. G. Wilson v, Letter to N. J. A. Sloane, Oct. 1993

Crossrefs

Cf. A000142, A007917.

Programs

Mathematica

PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; k ]; Table[ PrevPrime[ n! ], {n, 3, 25} ]
Join[{2},NextPrime[Range[3,30]!,-1]] (* Harvey P. Dale, Jan 24 2014 *)

Extensions

More terms from Jud McCranie; also from Robert G. Wilson v, Jan 03 2001