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

0,2

Links

Table of n, a(n) for n=0..104.

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.

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

Example

0.1418970546041639228128516171...

Mathematica

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

Prog

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

Crossrefs

Cf. A073000, A105531.

Sequence in context: A122914 A245566 A016689 * A179193 A124848 A090219

Adjacent sequences: A105530 A105531 A105532 * A105534 A105535 A105536

Keyword

cons,nonn

Author

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

Status

approved