

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.
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 AdrienMarie Legendre's guess.


REFERENCES

Panaitopol, L., Several Approximations of pi, Math. Ineq. Appl. 2(1999), 317324.
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 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 A132035
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



