

A054415


Smallest prime factor of n!1 (for n>2), a(2)=1.


6



1, 5, 23, 7, 719, 5039, 23, 11, 29, 13, 479001599, 1733, 87178291199, 17, 3041, 19, 59, 653, 124769, 23, 109, 51871, 625793187653, 149, 20431, 29, 239, 31, 265252859812191058636308479999999, 787
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OFFSET

2,2


COMMENTS

The initial term a(2)=1 is not a prime, but it does not affect search results and may prevent submission of duplicates.  M. F. Hasler, Oct 31 2012


LINKS

Table of n, a(n) for n=2..31.
P. Erdős and C. L. Stewart, On the greatest and least prime factors of n! + 1, J. London Math. Soc. (2) 13:3 (1976), pp. 513519.
M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 2426 (but beware errors). [Annotated scanned copy]
Hisanori Mishima, Factorizations of many number sequences: n!  1 (n = 1 to 100); Primorials  1.
R. G. Wilson v, Explicit factorizations


FORMULA

Erdős & Stewart show that a(n) > n + (lo(l))log n/log log n except when n+1 is prime, and that a(n) > n + e(n)sqrt(n) for almost all n where e(n) is any function with lim e(n) = 0.  Charles R Greathouse IV, Dec 05 2012


EXAMPLE

a(3)=5 because 3!1=5 which is prime; a(5)=7 because 5!1=119=7*17 and 7<17


MATHEMATICA

Do[ Print[ FactorInteger[ n!  1, FactorComplete > True][ [1, 1] ] ], {n, 3, 32} ]


PROG

(PARI) A054415(n)=if(n>2, factor(n!1)[1, 1], 1) \\  M. F. Hasler, Oct 31 2012


CROSSREFS

Cf. A002582, A033312, A051301.
Sequence in context: A282688 A282875 A317679 * A156328 A078190 A081319
Adjacent sequences: A054412 A054413 A054414 * A054416 A054417 A054418


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 10 2000


EXTENSIONS

More terms from Robert G. Wilson v, Aug 01 2000


STATUS

approved



