A057835 Difference between pi(10^n) and the integer nearest to 10^n / log(10^n).

0, 3, 23, 143, 906, 6116, 44158, 332774, 2592592, 20758029, 169923159, 1416705193, 11992858452, 102838308636, 891604962452, 7804289844393, 68883734693928, 612483070893536, 5481624169369961, 49347193044659702, 446579871578168707, 4060704006019620994, 37083513766578631309, 339996354713708049069, 3128516637843038351228

Offset: 1

Author

Robert G. Wilson v, Nov 08 2000

Keywords

• nonn

References

• John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1995, Page 146.

Links

• Eduard Roure Perdices, Table of n, a(n) for n = 1..28
• Wikipedia, Prime number theorem

Programs

Mathematica

Table[ PrimePi[10^n] - Round[ N[ 10^n/Log[ 10^n ] ] ], {n, 1, 13} ]

PARI

a(n)=primepi(10^n)-round(10^n/log(10^n)) \\ Charles R Greathouse IV, Mar 22 2015

Formula

a(n) = A006880(n) - A057834(n). - Henry Bottomley, Aug 10 2005

a(n) ~ 10^n/(n log 10)^2. - Charles R Greathouse IV, Mar 22 2015

Extensions

More terms from Jud McCranie, Jun 21 2005

Corrected and extended by Henry Bottomley, Aug 10 2005

a(22) to a(25) from Vladimir Pletser, Aug 10 2013