|
| |
|
|
A052435
|
|
Round(li(n) - pi(n)), where li is the logarithmic integral and pi(x) is the number of primes up to x.
|
|
6
| |
|
|
0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,8
|
|
|
COMMENTS
| Eventually contains negative terms!
The logarithmic integral is the "American" version starting at 0.
The first crossover (P. Demichel) is expected to be around 1.397162914*10^316. - Daniel Forgues, Oct 29 2011
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n = 2..20000
C. Caldwell, How many primes are there?
Patrick Demichel, The prime counting function and related subjects, April 05, 2005, 75 pages.
Eric Weisstein's World of Mathematics, Prime Counting Function
Eric Weisstein's World of Mathematics, Logarithmic Integral
Eric Weisstein's World of Mathematics, Skewes Number
|
|
|
MATHEMATICA
| Table[Round[LogIntegral[x]-PrimePi[x]], {x, 2, 100}]
|
|
|
PROG
| (PARI) a(n)=round(-eint1(-log(n))-primepi(n)) \\ Charles R Greathouse IV, Oct 28 2011
|
|
|
CROSSREFS
| Cf. A052434.
Sequence in context: A036238 A063982 A055020 * A094701 A054715 A145443
Adjacent sequences: A052432 A052433 A052434 * A052436 A052437 A052438
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
|
| |
|
|
