OFFSET
0,2
COMMENTS
Legendre's constant is 1.08366 (A228211). - Alonso del Arte, Nov 02 2013
This sequence has historical rather than mathematical interest, cf. A228211. It is better to use 1 + 1/log(10^n) instead of A. Since A is given to only 5 decimal places, it does not make much sense to compute terms of this sequence beyond n ~ 10. For n = 9, the error a(9)/A006880(9) is about 0.14%, while the error for 1 + 1/log(10^9) instead of A is only about 0.04%. - M. F. Hasler, Dec 03 2018
REFERENCES
Jan Gullberg, "Mathematics, From the Birth of Numbers", W. W. Norton and Company, NY and London, 1997, page 81.
LINKS
Eduard Roure Perdices, Table of n, a(n) for n = 0..28 (terms 0..23 from Harry J. Smith).
FORMULA
a(n) = round(10^n/(log(10^n) - 1.08366)) - A006880(n). - M. F. Hasler, Dec 03 2018
MATHEMATICA
Table[ Round[ 10^n /(Log[10^n] - 1.08366) - PrimePi[10^n] ], {n, 0, 13} ]
PROG
(PARI) {A006880_vec = [0, 4, 25, 168, 1229, 9592, 78498, 664579, 5761455, 50847534, 455052511 4118054813, 37607912018, 346065536839, 3204941750802, 29844570422669, 279238341033925, 2623557157654233, 24739954287740860, 234057667276344607, 2220819602560918840, 21127269486018731928, 201467286689315906290, 1925320391606803968923]} \\ Edited by M. F. Hasler, Dec 03 2018
{default(realprecision, 100); t=log(10); for (n=0, 23, write("b058290.txt", n, " ", round(10^n/(n*t - 1.08366)) - A006880_vec[n+1]))} \\ Harry J. Smith, Jun 22 2009
(PARI) A058290(n)={10^n\/(n*log(10)-1.08366)-A006880(n)} \\ with A006880(n)=primepi(10^n) and/or precomputed values for n > 10. - M. F. Hasler, Dec 03 2018
CROSSREFS
KEYWORD
sign,less
AUTHOR
Robert G. Wilson v, Dec 07 2000
EXTENSIONS
More terms from Harry J. Smith, Jun 22 2009
STATUS
approved