A084895 Decimal expansion of agm(1, 3), the arithmetic-geometric mean of 1 and 3.

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

Offset: 1

Author

Eric W. Weisstein, Jun 10 2003

Keywords

• nonn
• cons
• easy

Examples

			1.8636167832448965423556890310242705951575328568268537222204412269783257945...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean.
• Wikipedia, Arithmetic-geometric mean.

Crossrefs

Cf. A068521 (agm(1,2)), A084896 (agm(1,4)), A084897 (agm(1,5)), A000796, A249282.

Programs

Maple

evalf(GaussAGM(1, 3), 144);  # Alois P. Heinz, Jul 04 2023

Mathematica

RealDigits[ArithmeticGeometricMean[1, 3], 10, 120][[1]] (* Vincenzo Librandi, Mar 12 2015 *)
RealDigits[N[Pi/EllipticK[1/4], 102]][[1]] (* Jean-François Alcover, Jun 02 2019 *)

PARI

agm(1, 3) \\ Michel Marcus, Jun 02 2019

PARI

Pi/ellK(1/2) \\ Charles R Greathouse IV, Feb 04 2025

Formula

Equals Pi/EllipticK(1/4) = A000796 / A249282. - Amiram Eldar, Apr 28 2025