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A105534 Decimal expansion of arctan 1/239. 1
0, 0, 4, 1, 8, 4, 0, 7, 6, 0, 0, 2, 0, 7, 4, 7, 2, 3, 8, 6, 4, 5, 3, 8, 2, 1, 4, 9, 5, 9, 2, 8, 5, 4, 5, 2, 7, 4, 1, 0, 4, 8, 0, 6, 5, 3, 0, 7, 6, 3, 1, 9, 5, 0, 8, 2, 7, 0, 1, 9, 6, 1, 2, 8, 8, 7, 1, 8, 1, 7, 7, 8, 3, 4, 1, 4, 2, 2, 8, 9, 3, 2, 7, 3, 7, 8, 2, 6, 0, 5, 8, 1, 3, 6, 2, 2, 9, 0, 9, 4, 5, 4, 9, 7, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Comment from Frank Ellermann, Mar 01 2020: (Start)

8*A195790 - arctan( 1/239 ) - 4*arctan( 1/515 ) = Pi/4 (Meissel, Klingenstierna).

12*arctan( 1/18 ) + 8*arctan( 1/57 ) - 5*arctan( 1/239 ) = Pi/4 (Gauss). (End)

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

4*A105532 - arctan(1/239) = Pi/4 (Machin's formula).

EXAMPLE

0.0041840760020747238645382149...

MATHEMATICA

len = 103; n = RealDigits[N[ArcTan[1/239], len]]; PadLeft[First@ n, len + Abs@ Last@ n] (* Michael De Vlieger, Sep 14 2015 *)

Join[{0, 0}, RealDigits[ArcTan[1/239], 10, 120][[1]]] (* Harvey P. Dale, Apr 29 2016 *)

PROG

(PARI) atan(1/239) \\ Michel Marcus, Sep 24 2014

CROSSREFS

Cf. A003881 (Pi/4), A021243 (1/239), A105532 (arctan 1/5), A195790 (arccot 10).

Sequence in context: A201661 A263498 A198314 * A021243 A096051 A060440

Adjacent sequences:  A105531 A105532 A105533 * A105535 A105536 A105537

KEYWORD

cons,nonn

AUTHOR

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

STATUS

approved

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Last modified November 28 02:22 EST 2020. Contains 338699 sequences. (Running on oeis4.)