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A228211 Decimal expansion of Legendre's constant. 1
1, 0, 8, 3, 6, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

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 to infinity A(n) = 1.08366 in pi(n) = n/(log(n) - A(n)).

EXAMPLE

A = 1.08366.

CROSSREFS

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

STATUS

approved

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Last modified September 16 04:49 EDT 2014. Contains 246796 sequences.