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A057754 Integer nearest to Li(10^n), where Li(x) = integral(0..x, dt/log(t)). 9
6, 30, 178, 1246, 9630, 78628, 664918, 5762209, 50849235, 455055615, 4118066401, 37607950281, 346065645810, 3204942065692, 29844571475288, 279238344248557, 2623557165610822, 24739954309690415, 234057667376222382 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
"Li[z] is central to the study of the distribution of primes in number theory. The logarithmic integral function is sometimes also denoted by Li(z). In some number-theoretical applications li(z) is defined as [integral from 2 to z of 1/log(t) dt], with no principal value taken. This differs from the definition used in 'Mathematica' by the constant li(2)."
LINKS
C. Caldwell, values of pi(x)
B. Riemann, On the Number of Prime Numbers 1859, last page (various transcripts)
Stephen Wolfram, The Mathematica 3 Book, 1996, Section 3.2.10: Special Functions.
FORMULA
a(n) = round( Li( 10^n )) = round( Ei( log( 10^n ))).
EXAMPLE
Li( 10^22 ) = 201467286691248261498.15... => a(22).
pi( 10^22 ) = 201467286689315906290.
MAPLE
seq(round(evalf(Li(10^n), 64)), n=1..19); # Peter Luschny, Mar 20 2019
MATHEMATICA
Table[Round[LogIntegral[10^n]], {n, 1, 25}]
PROG
(PARI) vector(25, n, round(real(-eint1(-log(10^n)))) ) \\ G. C. Greubel, May 17 2019
(Magma) [Round(LogIntegral(10^n)): n in [1..25]]; // G. C. Greubel, May 17 2019
(Sage) [round(li(10^n)) for n in (1..25)] # G. C. Greubel, May 17 2019
CROSSREFS
A052435( 10^n ) = a(n) - pi( 10^n ) for n > 0.
Sequence in context: A110706 A001341 A089896 * A001473 A334288 A063888
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Oct 30 2000
STATUS
approved

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Last modified April 21 16:46 EDT 2024. Contains 371874 sequences. (Running on oeis4.)