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A228211
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Decimal expansion of Legendre's constant (incorrect, the true value is 1, as in A000007).
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2
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OFFSET
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1,3
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COMMENTS
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Included in accordance with the OEIS policy of listing incorrect but published sequences. The correct value of this constant is 1, by the prime number theorem pi(x) ~ li(x) = x/(log(x) - 1 - 1/log(x) + O(1/log^2(x))), where li is the logarithmic integral.
Before the prime number theorem was proved, it was believed that there was a constant A not equal to 1 that needed to be inserted in the formula pi(n) ~ n/(log(n) - A) to make it more precise. This number was Adrien-Marie Legendre's guess.
Panaitopol proved that x/(log(x) - A), where A is this constant, is an upper bound for pi(x) when x > 10^6. - John W. Nicholson, Feb 26 2018
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REFERENCES
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Hans Riesel, Prime Numbers and Computer Methods for Factorization. New York: Springer (1994): 41 - 43.
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LINKS
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FORMULA
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Believed at one time to be lim_{n -> infinity} A(n) in pi(n) = n/(log(n) - A(n)).
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EXAMPLE
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A = 1.08366.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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