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

1,2

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

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A255952 A089950 A198797 * A232145 A079755 A197176

Adjacent sequences: A057832 A057833 A057834 * A057836 A057837 A057838

Keyword

nonn

Author

Robert G. Wilson v, Nov 08 2000

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

Status

approved