A006990 Largest prime <= n!. (Formerly M1541)

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

Offset

2,1

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

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 *)

Crossrefs

Cf. A000142, A007917.

Sequence in context: A279819 A249606 A003501 * A358608 A242227 A032182

Adjacent sequences: A006987 A006988 A006989 * A006991 A006992 A006993

Keyword

nonn

Author

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

Extensions

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

Status

approved