OFFSET
3,1
COMMENTS
The continued fraction is: 291, 44, 1, 6, 3, 17, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 3, 1, 4, 10, 13, 2, 3, 26, ..., . - Robert G. Wilson v, Jun 09 2007
Increasing partial quotients: 44, 66, 75, 239, 280, 563, 577, 938, 8243, 8674, 30243, 130392, 1564166, ..., at positions: 1, 74, 105, 190, 232, 382, 518, 1543, 1761, 2330, 12204, 34946, 41957, ... - Robert G. Wilson v, Jun 09 2007
The constant is equal to Sum_{n>=0} S_n, where S_n is the area of an n-dimensional sphere of unit radius. This constant and the constant of A128891 are connected by the equation Sum_{n>=0}S_n - 2*Pi*Sum{n>=0}V_n = 2, where V_n is the volume of an n-dimensional sphere of unit radius. - Philippe A.J.G. Chevalier, Dec 17 2015
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..5003
FORMULA
2*(1 + Pi*e^Pi*(1 + erf(sqrt(Pi)))).
EXAMPLE
291.0222898249729824484089300040636921153978386238850492613995903...
MATHEMATICA
RealDigits[ 2*(1 + Pi*E^Pi*(1 + Erf[Sqrt[Pi]])), 10, 111][[1]] (* Robert G. Wilson v, Jun 09 2007 *)
PROG
(MATLAB) 2*(1+pi*exp(pi)*(1+erf(sqrt(pi)))) \\ Altug Alkan, Nov 11 2015
(PARI) 2*(1+Pi*exp(Pi)*(2-erfc(sqrt(Pi)))) \\ Michel Marcus, Nov 11 2015
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Philippe Deléham, Apr 20 2007
EXTENSIONS
More terms from Robert G. Wilson v, Jun 09 2007
STATUS
approved