

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
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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 CharlesJacques de la ValleePoussin 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 SpringerVerlag, NY, 1995, Pages 143  146.


LINKS

Vladimir Pletser, Table of n, a(n) for n = 1..50
Soren Laing AletheiaZomlefer, Lenny Fukshansky, Stephan Ramon Garcia, The BatemanHorn Conjecture: Heuristics, History, and Applications, arXiv:1807.08899 [math.NT], 20182019. 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 A121394
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



