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 A082884 a(n) = smallest prime p for which (r-p)/log(p) < 1/n, where r is the next prime after p. 8
 11, 59, 419, 2999, 22037, 162821, 1202627, 8886329, 65660051, 485165279, 3584913989, 26489122349, 195729610331, 1446257064389, 10686474581831, 78962960185097, 583461742527491, 4311231547116551, 31855931757115889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Remark: the quotient can be larger than 1/n at much larger primes, many times. So p does not set record in "standard" sense, only sinks first below 1/n, i.e. smaller than any previous values, but not necessarily smaller than the following ones. See also illustration. LINKS FORMULA a(n)=min{prime(j): A001223(j)/log(prime(j)) < 1/n}, where prime(j)=A000040(j) is the j-th prime. EXAMPLE a(1)=p(5)=11 and (13-11)/log(11) = 0.8340... < 1/1. MATHEMATICA {eq=1, k=1}; Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s<1/k, k=k+1; Print[{k, n, Prime[n], s}]; eq=s], {n, 1, 100000000}] CROSSREFS Cf. A082862, A082885, A082886, A082888-A082891. Sequence in context: A164299 A253207 A241860 * A193230 A077036 A076604 Adjacent sequences:  A082881 A082882 A082883 * A082885 A082886 A082887 KEYWORD nonn AUTHOR Labos Elemer, Apr 17 2003 EXTENSIONS a(11)-a(19) from Donovan Johnson, Sep 09 2008 STATUS approved

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Last modified April 21 17:36 EDT 2021. Contains 343156 sequences. (Running on oeis4.)