

A137218


Decimal expansion of the argument of 1 + 2*i.


10



2, 0, 3, 4, 4, 4, 3, 9, 3, 5, 7, 9, 5, 7, 0, 2, 7, 3, 5, 4, 4, 5, 5, 7, 7, 9, 2, 3, 1, 0, 0, 9, 6, 5, 8, 4, 4, 1, 2, 7, 1, 2, 1, 7, 5, 3, 9, 7, 3, 6, 7, 3, 1, 7, 4, 2, 9, 8, 4, 0, 5, 3, 8, 4, 8, 7, 4, 1, 0, 6, 0, 6, 7, 3, 0, 8, 8, 4, 6, 2, 0, 4, 6, 1, 4, 6, 1, 7, 6, 9, 6, 6, 5, 5, 9, 4, 6, 4, 2, 6, 5, 4, 7, 6, 0
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OFFSET

1,1


COMMENTS

Gives closed forms for many arctangent values:
arctan(2) = Pi  a, arctan(1/2) = a  Pi/2,
arctan(3) = a  Pi/4, arctan(1/3) = 3Pi/4  a,
arctan(7) = 7Pi/4  2a, arctan(1/7) = 2a  5Pi/4,
arctan(4/3) = 2a  Pi and arctan(3/4) = 3Pi/2  2a.
Dihedral angle in the dodecahedron (radians).  R. J. Mathar, Mar 24 2012
Larger interior angle (in radians) of a golden rhombus; A105199 is the smaller interior angle.  Eric W. Weisstein, Dec 17 2018


LINKS

Rick L. Shepherd, Table of n, a(n) for n = 1..20000
Eric Weisstein's World of Mathematics, Golden Rhombus
Wikipedia, Dodecahedron


FORMULA

Equals Pi  arctan(2) = A000796  A105199 = 2*A195723.


EXAMPLE

2.0344439357957027354455779231...


MATHEMATICA

RealDigits[Pi  ArcTan[2], 10, 120][[1]] (* Harvey P. Dale, Aug 08 2014 *)


PROG

(PARI)
default(realprecision, 120);
acos(1/sqrt(5)) \\ or
arg(1+2*I) \\ Rick L. Shepherd, Jan 26 2014


CROSSREFS

Platonic solids' dihedral angles: A137914 (tetrahedron), A156546 (octahedron), A019669 (cube), A236367 (icosahedron).  Stanislav Sykora, Jan 23 2014
Cf. A242723 (same in degrees).
Cf. A105199 (smaller interior angle of the golden rhombus).
Sequence in context: A213859 A101336 A300001 * A087819 A290820 A278029
Adjacent sequences: A137215 A137216 A137217 * A137219 A137220 A137221


KEYWORD

cons,nonn


AUTHOR

Matt Rieckman (mjr162006(AT)yahoo.com), Mar 06 2008


EXTENSIONS

Corrected a typo in the sequence Matt Rieckman (mjr162006(AT)yahoo.com), Feb 05 2010
More terms from Rick L. Shepherd, Jan 26 2014


STATUS

approved



