A062089 Decimal expansion of Sierpiński's constant.
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
Offset: 1
Examples
2.5849817595792532170658935873831711600880516518526309173215...
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. [Note: Last 2 digits given at this link are incorrect. - _William Echols_, Jun 04 2025]
- 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.
Programs
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Mathematica
K=-Pi Log[Pi]+2 Pi EulerGamma+4 Pi Log[Gamma[3/4]];First@RealDigits[N[K,105]](* Ant King, Mar 02 2013 *)
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PARI
-Pi*log(Pi)+2*Pi*Euler+4*Pi*log(gamma(3/4))
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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
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