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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 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 Cf. A004018, A062083, A222882, A222883. Sequence in context: A094001 A309252 A020859 * A011201 A201772 A196605 Adjacent sequences: A062086 A062087 A062088 * A062090 A062091 A062092 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.)