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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 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.)