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A057834
Integer nearest to 10^n / log(10^n).
9
4, 22, 145, 1086, 8686, 72382, 620421, 5428681, 48254942, 434294482, 3948131654, 36191206825, 334072678387, 3102103442166, 28952965460217, 271434051189532, 2554673422960305, 24127471216847324, 228576043106974646
OFFSET
1,1
COMMENTS
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."
REFERENCES
John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1995, Pages 143 - 146.
LINKS
Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, Stephan Ramon Garcia, The Bateman-Horn Conjecture: Heuristics, History, and Applications, arXiv:1807.08899 [math.NT], 2018-2019. See Table 1 p. 6.
FORMULA
a(n) = A050499(A011557(n)). - Henry Bottomley, Aug 10 2005
MATHEMATICA
Table[ Round[ N[ 10^n / Log[ 10^n ] ] ], {n, 1, 22} ]
PROG
(Magma) [Round(10^n / Log(10^n)): n in [1..20]]; // Vincenzo Librandi, Jul 09 2015
CROSSREFS
Sequence in context: A134988 A081002 A222012 * A196795 A278396 A369617
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Nov 08 2000
EXTENSIONS
Corrected by Henry Bottomley, Aug 10 2005
STATUS
approved