A217713 Integer part of log(n)^2.

0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18

Offset

0,5

Comments

Limit_{n->oo} Prime(n) = n*log(n).

Limit_{n->oo} PrimePi(n) = n/log(n).

Then ratio lengths are:

Limit_{n->oo} Prime(n)/PrimePi(n) = n*log(n)/(n/log(n)) = log(n)^2.

Links

Table of n, a(n) for n=0..70.

Formula

a(n) = floor(log(n)^2).

Mathematica

Table[Floor[Log[n]^2], {n, 1, 100}]

Crossrefs

Cf. A111114.

Sequence in context: A062575 A073188 A269225 * A047740 A137687 A024745

Adjacent sequences: A217710 A217711 A217712 * A217714 A217715 A217716

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 21 2013

Status

approved