A222642 Integer nearest to (Li(n) - Li(sqrt(n))), where Li(x) = integral(0..x, dt/log(t)).

1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19

Offset

2,2

Comments

Challenge: find the smallest n for which pi(n) < a(n), where pi(n) is the prime counting function.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 2..10000

Wikipedia, Prime number theorem

Mathematica

Table[Round[LogIntegral[n] - LogIntegral@Sqrt[n]], {n, 2, 74}]

Prog

(PARI) a(n)=round(real(eint1(-log(n)/2)-eint1(-log(n)))) \\ Charles R Greathouse IV, Feb 27 2013

Crossrefs

Cf. A047743.

Sequence in context: A137214 A284726 A319951 * A081832 A034887 A192543

Adjacent sequences: A222639 A222640 A222641 * A222643 A222644 A222645

Keyword

nonn

Author

Arkadiusz Wesolowski, Feb 27 2013

Status

approved