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A228211 Decimal expansion of Legendre's constant (incorrect, the true value is 1, as in A000007). 1
1, 0, 8, 3, 6, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

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) to make it correct. This number was Adrien-Marie Legendre's guess.

REFERENCES

Panaitopol, L., Several Approximations of pi,  Math. Ineq. Appl. 2(1999), 317-324.

Hans Riesel, Prime Numbers and Computer Methods for Factorization. New York: Springer (1994): 41 - 43.

LINKS

Table of n, a(n) for n=1..6.

Kevin Brown, Legendre's Prime Number Conjecture.

Eric W. Weisstein, "Legendre's Constant". From MathWorld--A Wolfram Web Resource.

FORMULA

Believed at one time to be lim_{n -> infinity} A(n) in pi(n) = n/(log(n) - A(n)).

EXAMPLE

A = 1.08366.

CROSSREFS

Cf. A000007.

Sequence in context: A124599 A005601 A104697 * A010522 A197332 A258991

Adjacent sequences:  A228208 A228209 A228210 * A228212 A228213 A228214

KEYWORD

nonn,cons

AUTHOR

Alonso del Arte, Nov 02 2013

EXTENSIONS

Edited by N. J. A. Sloane, Nov 13 2014

STATUS

approved

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Last modified July 4 09:43 EDT 2015. Contains 259200 sequences.