OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 122-126.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..5000
Steven R. Finch, Sierpinski's Constant. [Broken link]
Steven R. Finch, Sierpinski's Constant. [From the Wayback machine]
Simon Plouffe, Sierpinski Constant to 2000 digits.
Wacław Sierpiński, O sumowaniu szeregu Sigma_{n>a}^{n<=b} tau(n) f(n), gdzie tau(n) oznacza liczbę rozkładów liczby n na sumę kwadratów dwóch liczb całkowitych, Prace Matematyczno-Fizyczne, Vol. 18, No. 1 (1907), pp. 1-59.
Eric Weisstein's World of Mathematics, Sierpiński Constant.
Wikipedia, Sierpiński's 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
KEYWORD
AUTHOR
Jason Earls, Jun 27 2001
STATUS
approved