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A062089 Decimal expansion of Sierpiński's constant. 11
2, 5, 8, 4, 9, 8, 1, 7, 5, 9, 5, 7, 9, 2, 5, 3, 2, 1, 7, 0, 6, 5, 8, 9, 3, 5, 8, 7, 3, 8, 3, 1, 7, 1, 1, 6, 0, 0, 8, 8, 0, 5, 1, 6, 5, 1, 8, 5, 2, 6, 3, 0, 9, 1, 7, 3, 2, 1, 5, 4, 4, 9, 8, 7, 9, 7, 1, 9, 3, 2, 0, 4, 4, 0, 0, 1, 1, 5, 7, 1, 2, 0, 2, 1, 1, 1, 1, 7, 7, 2, 4, 5, 2, 7, 0, 6, 4, 2, 8, 3, 0, 3, 1, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 122-126.
LINKS
Steven R. Finch, Sierpinski's Constant. [Broken link]
Steven R. Finch, Sierpinski's Constant. [From the Wayback machine]
Eric Weisstein's World of Mathematics, Sierpiński Constant.
FORMULA
Equals -Pi*log(Pi)+2*Pi*gamma+4*Pi*log(GAMMA(3/4)).
Equals Pi*A241017. - Eric W. Weisstein, Dec 10 2014
Equals Pi*(A086058-1). - Eric W. Weisstein, Dec 10 2014
Equals lim_{n->oo} (A004018(n)/n - Pi*log(n)). - Amiram Eldar, Apr 15 2021
EXAMPLE
2.5849817595792532170658935873831711600880516518526309173215...
MATHEMATICA
K=-Pi Log[Pi]+2 Pi EulerGamma+4 Pi Log[Gamma[3/4]]; First@RealDigits[N[K, 105]](* Ant King, Mar 02 2013 *)
PROG
(PARI) -Pi*log(Pi)+2*Pi*Euler+4*Pi*log(gamma(3/4))
(PARI) { default(realprecision, 5080); x=-Pi*log(Pi)+2*Pi*Euler+4*Pi*log(gamma(3/4)); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b062089.txt", n, " ", d)) } \\ Harry J. Smith, Aug 01 2009
CROSSREFS
Sequence in context: A094001 A309252 A020859 * A011201 A201772 A196605
KEYWORD
cons,easy,nonn
AUTHOR
Jason Earls, Jun 27 2001
STATUS
approved

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Last modified February 27 21:03 EST 2024. Contains 370378 sequences. (Running on oeis4.)