A105532 Decimal expansion of arctan(1/5).

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

Offset: 0

Author

Bryan Jacobs (bryanjj(AT)gmail.com), Apr 12 2005

Keywords

• cons
• nonn

Examples

			0.197395559849880758370049765194790293447585103787852101517688940241033969...
		

Links

• Eric Weisstein's World of Mathematics, Machin-Like Formulas
• Index entries for transcendental numbers

Crossrefs

Cf. A003881 (Pi/4), A072172, A105534 (arctan 1/239).

Programs

Mathematica

RealDigits[ArcTan[1/5], 10, 100][[1]] (* Amiram Eldar, Aug 04 2020 *)

PARI

atan(1/5) \\ Michel Marcus, Sep 24 2014

Formula

4*arctan(1/5) - A105534 = Pi/4 (Machin's formula).

From Amiram Eldar, Aug 04 2020: (Start)

Equals Sum_{k>=0} (-1)^k/((2*k+1) * 5^(2*k+1)) = Sum_{k>=0} (-1)^k/A072172(k).

Equals Sum_{k>=1} arctan(1/(2*(k+2)^2)). (End)

Extensions

Corrected position of decimal point in example. - R. J. Mathar, Feb 05 2009