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 A228211 Decimal expansion of Legendre's constant (incorrect, the true value is 1, as in A000007). 1
 1, 0, 8, 3, 6, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Included in accordance with the OEIS policy of listing incorrect but published sequences. The correct value of this constant is 1, by the prime number theorem pi(x) ~ li(x) = x/(log(x) - 1 - 1/log(x) + O(1/log^2(x))), where li is the logarithmic integral. Before the prime number theorem was proved, it was believed that there was a constant A not equal to 1 that needed to be inserted in the formula pi(n) ~ n/(log(n) - A) to make it more precise. This number was Adrien-Marie Legendre's guess. Panaitopol proved that x/(log(x) - A), where A is this constant, is an upper bound for pi(x) when x > 10^6. - John W. Nicholson, Feb 26 2018 REFERENCES Hans Riesel, Prime Numbers and Computer Methods for Factorization. New York: Springer (1994): 41 - 43. LINKS Kevin Brown, Legendre's Prime Number Conjecture. Alexei Kourbatov, On the distribution of maximal gaps between primes in residue classes, arXiv:1610.03340 [math.NT], 2016-2017. Laurenţiu Panaitopol, Several Approximations of pi(x), Math. Ineq. Appl. 2(1999), 317-324. Eric Weisstein's World of Mathematics, "Legendre's Constant". FORMULA Believed at one time to be lim_{n -> infinity} A(n) in pi(n) = n/(log(n) - A(n)). EXAMPLE A = 1.08366. CROSSREFS Cf. A000007. Sequence in context: A304580 A304583 A104697 * A010522 A197332 A258991 Adjacent sequences:  A228208 A228209 A228210 * A228212 A228213 A228214 KEYWORD nonn,cons,fini,full AUTHOR Alonso del Arte, Nov 02 2013 EXTENSIONS Edited by N. J. A. Sloane, Nov 13 2014 STATUS approved

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Last modified June 17 15:07 EDT 2019. Contains 324185 sequences. (Running on oeis4.)