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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 (list; graph; refs; listen; history; text; internal format)
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

Amiram Eldar, Table of n, a(n) for n = 2..135

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. 513-519.

M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (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 + (l-o(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,changed

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

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)