

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, 263130836933693530167218012159999999, 8683317618811886495518194401279999999
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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

Chai Wah Wu, Table of n, a(n) for n = 2..153 (n = 2..135 from Amiram Eldar)
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
More terms from Amiram Eldar, Oct 07 2019


STATUS

approved



