

A124147


Primes p smaller than sqrt(g)*exp(sqrt(g)), where g is the gap between p and the next prime.


1



2, 3, 5, 7, 13, 23, 113, 1327, 31397, 370261, 2010733, 20831323, 25056082087
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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.  Robert G. Wilson v, Dec 30 2006


LINKS

Table of n, a(n) for n=1..13.
Eric Weisstein's World of Mathematics, Prime Gaps


EXAMPLE

a(9)=31397 because g=72 and sqrt(g)*exp(sqrt(g))=41093.88... > 31397.


MATHEMATICA

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, Dec 30 2006 *)


CROSSREFS

Cf. A000040, A001223, A000230.
Sequence in context: A080190 A076994 A327591 * A227627 A135372 A037021
Adjacent sequences: A124144 A124145 A124146 * A124148 A124149 A124150


KEYWORD

nonn,more


AUTHOR

Rémi Eismann, Dec 13 2006


EXTENSIONS

a(13) from Robert G. Wilson v, Dec 30 2006


STATUS

approved



