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%I #59 Apr 15 2021 05:25:19
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sierpiński's constant.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 122-126.
%H Harry J. Smith, <a href="/A062089/b062089.txt">Table of n, a(n) for n = 1..5000</a>
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/srp/srp.html">Sierpinski's Constant</a>. [Broken link]
%H Steven R. Finch, <a href="http://web.archive.org/web/20010207201533/http://www.mathsoft.com:80/asolve/constant/srp/srp.html">Sierpinski's Constant</a>. [From the Wayback machine]
%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/sierpinski.txt">Sierpinski Constant to 2000 digits</a>.
%H Wacław Sierpiński, <a href="https://eudml.org/doc/215235">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</a>, Prace Matematyczno-Fizyczne, Vol. 18, No. 1 (1907), pp. 1-59.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiConstant.html">Sierpiński Constant</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski%27s_constant">Sierpiński's constant</a>.
%F Equals -Pi*log(Pi)+2*Pi*gamma+4*Pi*log(GAMMA(3/4)).
%F Equals Pi*A241017. - _Eric W. Weisstein_, Dec 10 2014
%F Equals Pi*(A086058-1). - _Eric W. Weisstein_, Dec 10 2014
%F Equals lim_{n->oo} (A004018(n)/n - Pi*log(n)). - _Amiram Eldar_, Apr 15 2021
%e 2.5849817595792532170658935873831711600880516518526309173215...
%t K=-Pi Log[Pi]+2 Pi EulerGamma+4 Pi Log[Gamma[3/4]];First@RealDigits[N[K,105]](* _Ant King_, Mar 02 2013 *)
%o (PARI) -Pi*log(Pi)+2*Pi*Euler+4*Pi*log(gamma(3/4))
%o (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
%Y Cf. A004018, A062083, A222882, A222883.
%K cons,easy,nonn
%O 1,1
%A _Jason Earls_, Jun 27 2001
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