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Search: id:A082891
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| A082891 |
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Smallest prime p[j] such that quotient q[j], obtained when consecutive prime differences are divided by logarithm of smaller prime,p[j], is larger than n. |
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+0
8
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| 2, 7, 1129, 1327, 19609, 31397, 155921, 370261, 1357201, 2010881, 20831323, 20831323
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Is lim superior(q[n])=+infinity? See A082892.
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FORMULA
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a(n)=Min{p[x]; (p[x+1]-p[x])/log(p[x])>n}
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EXAMPLE
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n=1319945:p[n+1]=20831533,p[n]=20831323,d=210,
log[20831321]=16.852,q=210/16.852=12.4615>12
and first for >11 too.
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MATHEMATICA
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Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>11, Print[{n, Prime[n], Prime[n+1], s, Log[Prime[n]]//N}]], {n, 1000000, 100000000}]
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CROSSREFS
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Cf. A082862, A082884-A082890.
Adjacent sequences: A082888 A082889 A082890 this_sequence A082892 A082893 A082894
Sequence in context: A065590 A051249 A056165 this_sequence A000653 A128847 A123180
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 17 2003
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