A181693 Decimal expansion of AGM(1-x,1+x), where x = 1/(10^27+1).

9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset

0,1

Comments

0.999999999...9999999999750000000...000004999999...9999991718750000000...000001312499... (see the first link).

Links

Table of n, a(n) for n=0..103.

Gerd Lamprecht, Almost Integer, Patterns in decimals.

Gerd Lamprecht, 10000 digit from A-646 in pi.gerdlamprecht.de database.

Formula

Equals Pi/(2*K(1/(10^27+1)^2)), where K is the complete elliptic integral of the first kind. - Bruno Berselli, Mar 07 2013

Example

0.99999999999999999999999999999999999999999999999999999975000000000000...

Mathematica

RealDigits[With[{x = 1/(10^27 + 1)}, ArithmeticGeometricMean[1-x, 1+x]], 10, 120][[1]] (* Amiram Eldar, Mar 22 2026 *)

Prog

(PARI) x=1/(10^27+1); agm(1-x, 1+x) \\ Charles R Greathouse IV, Mar 03 2016
(PARI) agm(sqrt(1-1/(10^27+1)^2), 1) \\ Charles R Greathouse IV, Mar 03 2016

Crossrefs

Sequence in context: A363120 A363021 A099646 * A271880 A180599 A291092

Adjacent sequences: A181690 A181691 A181692 * A181694 A181695 A181696

Keyword

cons,nonn,less

Author

Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Nov 05 2010

Status

approved