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 A242568 Least number k >= 0 such that (n!+k)/(n+k) is prime. 2
 0, 1, 110, 1, 5026, 10070, 362862, 1, 39916778, 34, 6227020774, 25152407, 1307674367970, 50917, 355687428095966, 256443711659, 121645100408831962, 1286, 51090942171709439958, 111014413076599, 25852016738884976639954, 51704033477769953279974 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,3 COMMENTS a(n) <= n!-2n for all n. See A242567. a(68) = 1526549. Since 2 is prime, we see that (n!+k)/(n+k) = 2 when k = n!-2n, which is an integer. Thus, a(n) will always be nonzero. However, it is uncertain whether there are smaller k-values besides n!-2n. LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 3..60 EXAMPLE (4!+1)/(4+1) = 5 is prime. Thus, a(4) = 1. PROG (PARI) a(n)=for(k=1, 5*10^6, s=(n!+k)/(n+k); if(floor(s)==s, if(ispseudoprime(s), return(k)))); n=1; while(n<100, print(a(n)); n += 1) CROSSREFS Cf. A242567. Sequence in context: A287469 A266217 A229084 * A278865 A281286 A278739 Adjacent sequences: A242565 A242566 A242567 * A242569 A242570 A242571 KEYWORD nonn AUTHOR Derek Orr, May 17 2014 EXTENSIONS a(11)-a(24) from Hiroaki Yamanouchi, Sep 29 2014 STATUS approved

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Last modified August 11 23:45 EDT 2024. Contains 375082 sequences. (Running on oeis4.)