

A302716


Decimal expansion of 2*sin(Pi/675).


3



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

2,1


COMMENTS

This constant appears in a historic problem posed by Adriaan van Roomen (Adrianus Romanus) in his Ideae mathematicae from 1593, solved by Viète. See the Havil reference, problem 4, pp. 6974. See also the comments, references and links in A302711.
The present identity is R(45, 2*sin(Pi/675)) = 2*sin(Pi/15) = A272534 = 0.415823381635518..., with a special case of monic Chebyshev polynomials of the first kind, named R, given in A127672.


REFERENCES

Julian Havil, The Irrationals, A Story of the Numbers You Can't Count On, Princeton University Press, Princeton and Oxford, 2012, pp. 6974.


LINKS

Table of n, a(n) for n=2..97.
Index entries for sequences related to Chebyshev polynomials.


FORMULA

This constant is 2*sin(Pi/675).


EXAMPLE

0.0093083890713223248278454073630973484911817874590184488122045378391206664762...


MATHEMATICA

RealDigits[2 Sin[Pi/675], 10, 111][[1]] (* Robert G. Wilson v, Apr 29 2018 *)


PROG

(PARI) 2*sin(Pi/675) \\ Altug Alkan, May 01 2018


CROSSREFS

Cf. A127672, A272534, A302711.
Sequence in context: A154901 A057823 A011461 * A198546 A160579 A134897
Adjacent sequences: A302713 A302714 A302715 * A302717 A302718 A302719


KEYWORD

nonn,cons,easy


AUTHOR

Wolfdieter Lang, Apr 29 2018


STATUS

approved



