|
| |
|
|
A051301
|
|
Smallest prime factor of n!+1.
|
|
10
| |
|
|
2, 2, 3, 7, 5, 11, 7, 71, 61, 19, 11, 39916801, 13, 83, 23, 59, 17, 661, 19, 71, 20639383, 43, 23, 47, 811, 401, 1697, 10888869450418352160768000001, 29, 14557, 31, 257, 2281, 67, 67411, 137, 37, 13763753091226345046315979581580902400000001
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Theorem: For any N, there is a prime > N. Proof: Consider any prime factor of N!+1.
Cf. Wilson's Theorem (1770): p | (p-1)! + 1 iff p is a prime.
|
|
|
REFERENCES
| Albert H. Beiler, "Recreations in The Theory of Numbers, The Queen of Mathematics Entertains," Dover Publ. NY, 1966, Page 49.
A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.
M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..100 (derived from Hisanori Mishima's data)
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
R. G. Wilson v, Explicit factorizations
|
|
|
MAPLE
| with(numtheory): A051301 := n -> sort(convert(divisors(n!+1), list))[2];
|
|
|
MATHEMATICA
| Do[ Print[ FactorInteger[ n! + 1, FactorComplete -> True ] [ [ 1, 1 ] ] ], {n, 0, 38} ]
|
|
|
CROSSREFS
| Cf. A002583, A038507, A096225.
Sequence in context: A123934 A203362 A183407 * A002583 A068519 A083702
Adjacent sequences: A051298 A051299 A051300 * A051302 A051303 A051304
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
|
|
|
EXTENSIONS
| Maple program corrected by Peter Luschny (peter(AT)luschny.de), Jul 17 2009
|
| |
|
|
