A105533 Decimal expansion of arctan(1/7).

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

Offset: 0

Author

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

Keywords

• cons
• nonn

Examples

			0.1418970546041639228128516171...
		

Links

• D. H. Lehmer, On Arccotangent Relations for π, The American Mathematical Monthly, Vol. 45, No. 10 (Dec., 1938), pp. 657-664.
• Eric Weisstein's World of Mathematics, Machin-Like Formulas.
• Index entries for transcendental numbers

Crossrefs

Cf. A073000, A105531.

Programs

Mathematica

RealDigits[ArcTan[1/7],10,120][[1]] (* Harvey P. Dale, Oct 03 2012 *)

PARI

atan(1/7) \\ Michel Marcus, Mar 01 2020

Formula

2*A073000 - arctan(1/7) = 2*A105531 + arctan(1/7) = Pi/4.

5*arctan(1/7) + 2*arctan(3/79) = Pi/4. - Frank Ellermann, Mar 01 2020

Equals arcsin(1/(5*sqrt(2))) = arccos(7/(5*sqrt(2))). - Amiram Eldar, Jul 11 2023