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A137218 Decimal expansion of the argument of -1 + 2*i. 6
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 (list; constant; graph; refs; listen; history; text; internal format)
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

LINKS

Rick L. Shepherd, Table of n, a(n) for n = 1..20000

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).

Sequence in context: A274441 A213859 A101336 * A087819 A278029 A066246

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

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Last modified December 11 08:45 EST 2016. Contains 279045 sequences.