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Search: id:A057754
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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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+0
4
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| 6, 30, 178, 1246, 9630, 78628, 664918, 5762209, 50849235, 455055615, 4118066401, 37607950281, 346065645810, 3204942065692, 29844571475288, 279238344248557, 2623557165610822, 24739954309690415, 234057667376222382
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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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.
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FORMULA
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a(n) = round( Li( 10^n )) = round( Ei( ln( 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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MATHEMATICA
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Table[ Round[ LogIntegral[ 10^n ] ], {n, 1, 25} ]
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CROSSREFS
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A052435( 10^n ) = a(n) - pi( 10^n ) for n > 0. Cf. A000720, A007504.
Sequence in context: A110706 A001341 A089896 this_sequence A001473 A063888 A029571
Adjacent sequences: A057751 A057752 A057753 this_sequence A057755 A057756 A057757
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 30 2000
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