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A195720
Decimal expansion of arccos(sqrt(1/6)) and of arcsin(sqrt(5/6)) and arctan(sqrt(5)).
4
1, 1, 5, 0, 2, 6, 1, 9, 9, 1, 5, 1, 0, 9, 3, 1, 4, 9, 1, 3, 4, 3, 0, 5, 9, 1, 7, 5, 7, 2, 6, 5, 3, 6, 0, 6, 8, 7, 4, 7, 5, 4, 5, 3, 0, 6, 8, 6, 7, 6, 3, 3, 3, 0, 0, 5, 9, 8, 2, 1, 0, 8, 9, 3, 8, 0, 7, 8, 6, 3, 5, 5, 1, 4, 0, 4, 9, 3, 5, 8, 1, 9, 0, 5, 4, 7, 5, 0, 4, 1, 0, 2, 4, 5, 2, 6, 6, 0, 1, 7
OFFSET
1,3
LINKS
Kunle Adegoke, Infinite arctangent sums involving Fibonacci and Lucas numbers, arXiv:1603.08097 [math.NT], 2016.
FORMULA
Equals Sum_{k >= 1} sqrt(5)/L(2n) where L=A000032. See also A005248. - Michel Marcus, Mar 29 2016
EXAMPLE
arccos(sqrt(1/6)) = 1.150261991510931...
MATHEMATICA
r = Sqrt[1/6]; RealDigits[ArcCos[r], 10, 100][[1]]
PROG
(PARI) atan(sqrt(5)) \\ Michel Marcus, Mar 29 2016
(Magma) [Arccos(Sqrt(1/6))]; // G. C. Greubel, Nov 23 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 23 2011
STATUS
approved