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#12 by Susanna Cuyler at Tue Aug 04 09:03:10 EDT 2020
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#11 by Michel Marcus at Tue Aug 04 03:39:01 EDT 2020
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#10 by Michel Marcus at Tue Aug 04 03:38:58 EDT 2020
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| NAME
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Decimal expansion of arctan (1/5.).
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| STATUS
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proposed
editing
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#9 by Amiram Eldar at Tue Aug 04 02:49:30 EDT 2020
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#8 by Amiram Eldar at Tue Aug 04 02:41:03 EDT 2020
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| FORMULA
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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)
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| MATHEMATICA
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RealDigits[ArcTan[1/5], 10, 100][[1]] (* Amiram Eldar, Aug 04 2020 *)
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| CROSSREFS
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Cf. A003881 (Pi/4), A072172, A105534 (arctan 1/239).
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| STATUS
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approved
editing
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#7 by Vaclav Kotesovec at Wed Sep 24 02:24:59 EDT 2014
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#6 by Michel Marcus at Wed Sep 24 01:44:08 EDT 2014
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#5 by Michel Marcus at Wed Sep 24 01:43:53 EDT 2014
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| COMMENTS
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4*arctan(1/5) - A105534 = pi/4
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| LINKS
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<Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Machin-LikeFormulas.html">Machin-Like Formulas from MathWorld</a>
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| FORMULA
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4*arctan(1/5) - A105534 = Pi/4 (Machin's formula).
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| EXAMPLE
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0.197395559849880758370049765194790293447585103787852101517688940241033969978243785732697828037288044112628197395559849880758370049765194790293447585103787852101517688940241033969...
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| PROG
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(PARI) atan(1/5) \\ Michel Marcus, Sep 24 2014
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| CROSSREFS
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Cf. A003881 (Pi/4), A105534 (arctan 1/239).
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| AUTHOR
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Bryan JaocbsJacobs (bryanjj(AT)gmail.com), Apr 12 2005
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| STATUS
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approved
editing
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#4 by Russ Cox at Fri Mar 30 17:39:05 EDT 2012
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| EXTENSIONS
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Corrected position of decimal point in example. - . - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Feb 05 2009
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Discussion
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| Fri Mar 30
| 17:39
| OEIS Server: https://oeis.org/edit/global/190
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#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010
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| KEYWORD
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cons,nonn,new
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| EXTENSIONS
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Corrected position of decimal dotpoint in example. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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