login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 09:38 EST 2014. Contains 250305 sequences.