|
Search: id:A057834
|
|
|
| A057834 |
|
Integer nearest to 10^n / log(10^n). |
|
+0
4
|
|
| 4, 22, 145, 1086, 8686, 72382, 620421, 5428681, 48254942, 434294482, 3948131654, 36191206825, 334072678387, 3102103442166, 28952965460217, 271434051189532, 2554673422960305, 24127471216847324, 228576043106974646
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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 guessed, 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.
|
|
FORMULA
|
((10^n)^2)/(ln((10^n)!)) [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Jul 15 2009]
a(n) = A050499(A011557(n)) - Henry Bottomley (se16(AT)btinternet.com), Aug 10 2005
|
|
MATHEMATICA
|
Table[ Round[ N[ 10^n / Log[ 10^n ] ] ], {n, 1, 22} ]
|
|
CROSSREFS
|
Sequence in context: A027391 A134988 A081002 this_sequence A121394 A005039 A112898
Adjacent sequences: A057831 A057832 A057833 this_sequence A057835 A057836 A057837
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 08 2000
|
|
EXTENSIONS
|
Corrected by Henry Bottomley (se16(AT)btinternet.com), Aug 10 2005
|
|
|
Search completed in 0.002 seconds
|
