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Search: id:A124147
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| A124147 |
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Primes p smaller than sqrt(g)*exp(sqrt(g)), where g is the gap between p and the next prime. |
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+0
1
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| 2, 3, 5, 7, 13, 23, 113, 1327, 31397, 370261, 2010733, 20831323, 25056082087
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Except for 5 & 13, all of the terms here are in A002386 "Increasing gaps between primes ..." at positions 1, 2, 3, 4, 6, 10, 14, 17, 21, 24 & 39. - (from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 30 2006)
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
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EXAMPLE
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a(9)=31397 because g=72 and sqrt(g)*exp(sqrt(g))=41093.88... > 31397.
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MATHEMATICA
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k] lst = {}; p = 2; Do[q = NextPrim@p; g = q - p; If[p < Sqrt[g]*Exp[Sqrt[g]], Print@p; AppendTo[lst, p]]; p = q, {n, 1235000000}] - Robert G. Wilson v (rgwv(at)rgwv.com), Dec 30 2006
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CROSSREFS
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Cf. A000040, A001223, A000230.
Adjacent sequences: A124144 A124145 A124146 this_sequence A124148 A124149 A124150
Sequence in context: A006992 A080190 A076994 this_sequence A135372 A103597 A037021
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KEYWORD
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nonn
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AUTHOR
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Remi Eismann (reismann(AT)free.fr), Dec 13 2006
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EXTENSIONS
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a(13) from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 30 2006
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