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 A058290 Rounded difference between 10^n/(log(10^n) - A) and pi(10^n), where A is Legendre's constant and pi is the prime counting function. 3
 -1, 4, 3, 4, 2, -4, 45, 561, 6549, 69985, 690493, 6545056, 60615397, 555560046, 5070271362, 46223804313, 421692578206, 3853431791690, 35289854434775, 323979090116197, 2981921009910364, 27516571651291205, 254562416350667928 (list; graph; refs; listen; history; text; internal format)
 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 Harry J. Smith, Table of n, a(n) for n=0,...,23 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 Cf. A006880, A057752, A057794, A057835, A058289. Sequence in context: A161882 A276789 A082125 * A002285 A106049 A238234 Adjacent sequences:  A058287 A058288 A058289 * A058291 A058292 A058293 KEYWORD sign,less AUTHOR Robert G. Wilson v, Dec 07 2000 EXTENSIONS More terms from Harry J. Smith, Jun 22 2009 STATUS approved

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Last modified May 29 14:18 EDT 2020. Contains 334700 sequences. (Running on oeis4.)