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a(n) = floor(prime(n) - n*(log(n) - log(log(n)) - 1)) for n>=2.
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%I #18 Mar 07 2015 16:48:11

%S 2,4,6,10,11,15,16,19,24,25,30,32,33,36,40,45,46,50,53,53,57,60,64,70,

%T 72,73,75,75,77,89,91,95,95,103,103,107,111,113,117,121,121,129,129,

%U 130,130,140,150,151,151,153,156,156,164,167,171,175,174,178,179,179,187

%N a(n) = floor(prime(n) - n*(log(n) - log(log(n)) - 1)) for n>=2.

%C Estimation involved seems (by experience) strongly improved because floor(prime(n)-log(n)-log(log(n)-3)) > 0 for large enough n.

%H P. Dusart, <a href="http://www.jstor.org/stable/2585122">The kth prime is greater than k(ln k + ln ln k-1) for k>=2</a>, Mathematics of Computation 68 (1999), pp. 411-415.

%t Table[Floor[Prime[w] - w (Log[w] - Log[Log[w]] - 1)//N], {w, 2, 256}]

%o (PARI) a(n) = floor(prime(n) - n*(log(n)-log(log(n))-1)); \\ _Michel Marcus_, Mar 04 2015

%Y Cf. A000040.

%K nonn

%O 2,1

%A _Labos Elemer_, Sep 17 2003