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

4, 22, 145, 1086, 8686, 72382, 620421, 5428681, 48254942, 434294482, 3948131654, 36191206825, 334072678387, 3102103442166, 28952965460217, 271434051189532, 2554673422960305, 24127471216847324, 228576043106974646

Offset: 1

Author

Robert G. Wilson v, Nov 08 2000

Keywords

• nonn

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

• Vladimir Pletser, Table of n, a(n) for n = 1..50
• 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.

Programs

Magma

[Round(10^n / Log(10^n)): n in [1..20]]; // Vincenzo Librandi, Jul 09 2015

Mathematica

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

Formula

a(n) = A050499(A011557(n)). - Henry Bottomley, Aug 10 2005

Extensions

Corrected by Henry Bottomley, Aug 10 2005