A086203 - OEIS

%I #18 Jan 14 2023 13:34:04

%S 1,4,7,5,8,3,6,1,7,6,5,0,4,3,3,2,7,4,1,7,5,4,0,1,0,7,6,2,2,4,7,4,0,5,

%T 2,5,9,5,1,1,3,4,5,2,3,8,8,6,9,1,7,8,9,4,5,9,9,9,2,2,3,1,2,8,6,2,7,1,

%U 1,4,7,6,7,8,6,0,2,6,3,3,6,7,3,1,7,1,4,2,9,8,9,4,7,7,8,9,8,0,4,0,0,7

%N Decimal expansion of arctan(1/2)/Pi.

%C This constant is a transcendental number (Margolius, 2002; Smith, 2003). - _Amiram Eldar_, Aug 13 2020

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See pp. 430-433.

%H Jonathan M. Borwein and Roland Girgensohn, <a href="https://doi.org/10.4153/CJM-1995-013-4">Addition Theorems and Binary Expansions</a>, Canadian Journal of Mathematics, Vol. 47, No. 2 (1995), pp. 262-273.

%H Barbara H. Margolius, <a href="https://web.archive.org/web/20191124180025/https://www.lacim.uqam.ca/~plouffe/articles/plouffe.pdf">Plouffe's Constant is Transcendental</a>, unpublished note, 2002.

%H Simon Plouffe, <a href="https://www.emis.de/journals/JIS/compass.html">The computation of certain numbers using a ruler and compass</a>, Journal of Integer Sequences, Vol. 1 (1998), Article 98.1.3.

%H Warren D. Smith, <a href="https://rangevoting.org/WarrenSmithPages/homepage/diophant.pdf">Pythagorean triples, rational angles, and space-filling simplices</a>, preprint, 2003.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlouffesConstants.html">Plouffe's Constants</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 0.14758...

%t RealDigits[ArcTan[1/2]/Pi, 10, 100][[1]] (* _Amiram Eldar_, Aug 13 2020 *)

%o (PARI)  atan(1/2)/Pi \\ _Michel Marcus_, Jul 29 2015

%Y Cf. A000796, A073000.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Jul 12 2003