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A057834 Integer nearest to 10^n / log(10^n). 9

%I

%S 4,22,145,1086,8686,72382,620421,5428681,48254942,434294482,

%T 3948131654,36191206825,334072678387,3102103442166,28952965460217,

%U 271434051189532,2554673422960305,24127471216847324,228576043106974646

%N Integer nearest to 10^n / log(10^n).

%C Legendre's Logarithmic Law: "In 1896, a full century after Adrienne Marie Legendre (1752 - 1833) guessed the approximate formula N/ln N for the number of primes up to N, Jacques Hadamard and Charles-Jacques de la Vallee-Poussin conclusively established it. They both lived for more than 50 years after producing their simultaneous but independent proofs." ... "In the meantime, Gauss and Riemann had made improved guesses expressed in terms of natural logarithms that we'll meet in Chapter 9."

%D John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1995, Pages 143 - 146.

%H Vladimir Pletser, <a href="/A057834/b057834.txt">Table of n, a(n) for n = 1..50</a>

%H Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, Stephan Ramon Garcia, <a href="https://arxiv.org/abs/1807.08899">The Bateman-Horn Conjecture: Heuristics, History, and Applications</a>, arXiv:1807.08899 [math.NT], 2018-2019. See Table 1 p. 6.

%F a(n) = A050499(A011557(n)). - _Henry Bottomley_, Aug 10 2005

%t Table[ Round[ N[ 10^n / Log[ 10^n ] ] ], {n, 1, 22} ]

%o (MAGMA) [Round(10^n / Log(10^n)): n in [1..20]]; // _Vincenzo Librandi_, Jul 09 2015

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Nov 08 2000

%E Corrected by _Henry Bottomley_, Aug 10 2005

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)