

A228211


Decimal expansion of Legendre's constant (incorrect, the true value is 1, as in A000007).


1




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 pi(x) ~ li(x) = x/(log(x)  1  1/log(x) + O(1/log^2(x))).
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 AdrienMarie Legendre's guess.


REFERENCES

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.
L. Panaitopol, Several Approximations of pi(x), Math. Ineq. Appl. 2(1999), 317324.
Eric W. Weisstein, "Legendre's Constant". From MathWorldA 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,fini,full


AUTHOR

Alonso del Arte, Nov 02 2013


EXTENSIONS

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


STATUS

approved



