A086917 a(n) = floor(prime(n) - n*(log(n) - log(log(n)) - 1)) for n>=2.

2, 4, 6, 10, 11, 15, 16, 19, 24, 25, 30, 32, 33, 36, 40, 45, 46, 50, 53, 53, 57, 60, 64, 70, 72, 73, 75, 75, 77, 89, 91, 95, 95, 103, 103, 107, 111, 113, 117, 121, 121, 129, 129, 130, 130, 140, 150, 151, 151, 153, 156, 156, 164, 167, 171, 175, 174, 178, 179, 179, 187

Offset

2,1

Comments

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

Links

Table of n, a(n) for n=2..62.

P. Dusart, The kth prime is greater than k(ln k + ln ln k-1) for k>=2, Mathematics of Computation 68 (1999), pp. 411-415.

Mathematica

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

Prog

(PARI) a(n) = floor(prime(n) - n*(log(n)-log(log(n))-1)); \\ Michel Marcus, Mar 04 2015

Crossrefs

Cf. A000040.

Sequence in context: A249428 A129630 A026429 * A004789 A027435 A014666

Adjacent sequences: A086914 A086915 A086916 * A086918 A086919 A086920

Keyword

nonn

Author

Labos Elemer, Sep 17 2003

Status

approved