A364945 Decimal expansion of 1-Catalan.

0, 8, 4, 0, 3, 4, 4, 0, 5, 8, 2, 2, 7, 8, 0, 9, 8, 4, 9, 4, 5, 3, 9, 6, 4, 8, 5, 0, 6, 7, 6, 1, 5, 8, 8, 9, 2, 2, 5, 8, 5, 0, 6, 2, 5, 7, 1, 8, 3, 2, 7, 8, 6, 5, 7, 3, 3, 5, 0, 1, 8, 8, 0, 3, 7, 8, 2, 3, 6, 9, 8, 0, 2, 2, 3, 7, 4, 5, 2, 3, 0, 5, 2, 0, 6, 4, 3, 4, 8

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 56.

Links

Table of n, a(n) for n=0..88.

J. W. L. Glaisher, Numerical Values of the Series 1 - 1/3^n + 1/5^n - 1/7^n + 1/9^n - &c. For n = 2, 4, 6, Messenger of Mathematics, Vol. 42 (1913), pp. 50-58. [Available only in the USA through the Hathi Trust]

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 122.

Formula

Equals 3F2( -1/2,-1/2,1 ; 1/2,1/2 ; -1) = (1/4) * Sum_{k>=0} (-1)^k/(k-1/2)^2.

Equals 1-A006752.

Equals Sum_{k>=1} k*zeta(2*k+1)/16^k (Glaisher, 1913). - Amiram Eldar, Aug 14 2023

Equals Sum_{k>=1} 16*k/(16*k^2 - 1)^2 = Integral_{x=1..oo} log(x)/(x^4 + x^2) dx (see Shamos). - Stefano Spezia, Nov 14 2024

Example

0.084034405822780984945396...

Maple

evalf(1-Catalan) ;

Mathematica

RealDigits[1 - Catalan, 10, 120, -1][[1]] (* Amiram Eldar, Aug 14 2023 *)

Prog

(PARI) 1 - Catalan \\ Michel Marcus, Aug 14 2023

Crossrefs

Cf. A006752.

Sequence in context: A200108 A088397 A021123 * A354632 A114313 A096616

Adjacent sequences: A364942 A364943 A364944 * A364946 A364947 A364948

Keyword

nonn,cons

Author

R. J. Mathar, Aug 14 2023

Status

approved