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A057754
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Integer nearest to Li(10^n), where Li(x) = integral(0..x, dt/log(t)).
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9
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6, 30, 178, 1246, 9630, 78628, 664918, 5762209, 50849235, 455055615, 4118066401, 37607950281, 346065645810, 3204942065692, 29844571475288, 279238344248557, 2623557165610822, 24739954309690415, 234057667376222382
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OFFSET
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1,1
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COMMENTS
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"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)."
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LINKS
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FORMULA
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a(n) = round( Li( 10^n )) = round( Ei( log( 10^n ))).
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EXAMPLE
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Li( 10^22 ) = 201467286691248261498.15... => a(22).
pi( 10^22 ) = 201467286689315906290.
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MAPLE
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seq(round(evalf(Li(10^n), 64)), n=1..19); # Peter Luschny, Mar 20 2019
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MATHEMATICA
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Table[Round[LogIntegral[10^n]], {n, 1, 25}]
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PROG
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(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
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CROSSREFS
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A052435( 10^n ) = a(n) - pi( 10^n ) for n > 0.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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