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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 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. 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 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 May 14 19:38 EDT 2021. Contains 343902 sequences. (Running on oeis4.)