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

1,1

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

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.

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

Adjacent sequences: A057831 A057832 A057833 * A057835 A057836 A057837

Keyword

nonn

Author

Robert G. Wilson v, Nov 08 2000

Extensions

Corrected by Henry Bottomley, Aug 10 2005

Status

approved