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Search: id:A082884
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| A082884 |
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a(n) = smallest prime p for which (r-p)/log(p) < 1/n, where r is the next prime after p. |
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+0
9
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| 11, 59, 419, 2999, 22037, 162821, 1202627, 8886329, 65660051, 485165279, 3584913989, 26489122349, 195729610331, 1446257064389, 10686474581831, 78962960185097, 583461742527491, 4311231547116551, 31855931757115889
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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FORMULA
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a(n)=min{prime(j): A001223(j)/log(prime(j)) < 1/n}, where prime(j)=A000040(j) is the j-th prime.
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EXAMPLE
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a(1)=p(5)=11 and (13-11)/log(11) = 0.8340... < 1/1.
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MATHEMATICA
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{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}]
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CROSSREFS
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Cf. A082862, A082885, A082886, A082888-A082891.
Sequence in context: A142401 A139859 A164299 this_sequence A077036 A076604 A076676
Adjacent sequences: A082881 A082882 A082883 this_sequence A082885 A082886 A082887
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 17 2003
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EXTENSIONS
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a(11)-a(19) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 09 2008
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