A058289 Integer nearest 10^n/(log(10^n) - 1.08366).

-1, 8, 28, 172, 1231, 9588, 78543, 665140, 5768004, 50917519, 455743004, 4124599869, 37668527415, 346621096885, 3210012022164, 29890794226982, 279660033612131, 2627410589445923, 24775244142175635, 234381646366460804

Offset: 0

Author

Robert G. Wilson v, Dec 07 2000

Keywords

• sign

Comments

"Adrien-Marie Legendre in 1778 published his work 'Essai sur la théorie des nombres' where he proposed a modified form of the first approximation, pi(n) ~ n/ln n." (Gullberg)

References

• Jan Gullberg, "Mathematics, From the Birth of Numbers," W. W. Norton and Company, NY and London, 1997, page 80.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A006880, A057754, A057793, A057834, A058290.

Programs

Mathematica

Table[ Round[ 10^n /(Log[10^n] - 1.08366) ], {n, 0, 22} ]

PARI

{ default(realprecision, 1000); t=log(10); for (n=0, 500, write("b058289.txt", n, " ", round(10^n/(n*t - 1.08366))); ); } \\ Harry J. Smith, Jun 22 2009

Extensions

Corrected some terms. - Harry J. Smith, Jun 22 2009