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

1,1

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