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A057752
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Difference between nearest integer to Li(10^n) and pi(10^n), where Li(x) = integral of log(x) and pi(10^n) = number of primes <= 10^n (A006880).
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10
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2, 5, 10, 17, 38, 130, 339, 754, 1701, 3104, 11588, 38263, 108971, 314890, 1052619, 3214632, 7956589, 21949555, 99877775, 222744644, 597394254, 1932355208, 7250186216, 17146907278, 55160980939, 155891678121, 508666658006, 1427745660374, 4551193622464
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OFFSET
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1,1
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COMMENTS
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On his prime pages C. K. Caldwell remarks: "However in 1914 Littlewood proved that pi(x)-Li(x) assumes both positive and negative values infinitely often". - Frank Ellermann, May 31 2003
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REFERENCES
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John H. Conway and R. K. Guy, The Book of Numbers, Copernicus, an imprint of Springer-Verlag, NY, 1995, page 146.
Marcus du Sautoy, The Music of the Primes, Fourth Estate / HarperCollins, 2003; see table on p. 90.
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LINKS
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MATHEMATICA
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Table[Round[LogIntegral[10^n] - PrimePi[10^n]], {n, 1, 13}]
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PROG
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(Python)
from sympy import N, li, primepi, floor
def round(n):
return int(floor(n+0.5))
return round(N(li(10**n), 10*n)) - primepi(10**n) # Chai Wah Wu, Apr 30 2018
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CROSSREFS
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KEYWORD
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sign,hard
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AUTHOR
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EXTENSIONS
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The value of a(23) is not known at present, I believe. - N. J. A. Sloane, Mar 17 2008
Name corrected and extended for last two terms a(23) and a(24), with Pi(10^n) for n=23 and 24 from A006880, by Vladimir Pletser, Mar 10 2013
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STATUS
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approved
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