

A161011


Decimal expansion of tan(1/2).


4



5, 4, 6, 3, 0, 2, 4, 8, 9, 8, 4, 3, 7, 9, 0, 5, 1, 3, 2, 5, 5, 1, 7, 9, 4, 6, 5, 7, 8, 0, 2, 8, 5, 3, 8, 3, 2, 9, 7, 5, 5, 1, 7, 2, 0, 1, 7, 9, 7, 9, 1, 2, 4, 6, 1, 6, 4, 0, 9, 1, 3, 8, 5, 9, 3, 2, 9, 0, 7, 5, 1, 0, 5, 1, 8, 0, 2, 5, 8, 1, 5, 7, 1, 5, 1, 8, 0, 6, 4, 8, 2, 7, 0, 6, 5, 6, 2, 1, 8, 5, 8, 9, 1, 0, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

By the LindemannWeierstrass theorem, this constant is transcendental.  Charles R Greathouse IV, May 13 2019


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000
MathOverflow, What is the effect of adding 1/2 to a continued fraction?
Wikipedia, LindemannWeierstrass theorem
Index entries for transcendental numbers


FORMULA

From Peter Bala, Nov 17 2019: (Start)
Related simple continued fraction expansions:
tan(1/2) = [0; 1, 1, 4, 1, 8, 1, 12, 1, 16, 1, 20, 1, ...]. See A019425.
2*tan(1/2) = [1, 10, 1, 3, 1, 26, 1, 7, 1, 42, 1, 11, 1, 58, 1, 15, 1, 74, 1, 19, 1, 90, ...]
(1/2)*tan(1/2) = [0; 3, 1, 1, 1, 18, 1, 5, 1, 34, 1, 9, 1, 50, 1, 13, 1, 66, 1, 17, 1, 82, ...].
tan(1/2)/(1  tan(1/2)) = [1, 4, 1, 8, 1, 12, 1, 16, 1, 20, 1, 24, ...]
2*tan(1/2)/(1  tan(1/2)) = [2, 2, 2, 4, 2, 6, 2, 8, 2, 10, 2, 12, ...]
4*tan(1/2)/(1  tan(1/2)) = [4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, ...]. (End)


EXAMPLE

0.546302489843790513255179465780285383297551720179791246164091385932907...


MATHEMATICA

RealDigits[N[Tan[1/2], 6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2009 *)


PROG

(PARI) default(realprecision, 20080); x=10*tan(1/2); for (n=0, 20000, d=floor(x); x=(xd)*10; write("b161011.txt", n, " ", d));


CROSSREFS

Cf. A019425 (continued fraction). Cf. A049471, A161011 through A161019.
Sequence in context: A255291 A070365 A190613 * A232734 A298513 A021187
Adjacent sequences: A161008 A161009 A161010 * A161012 A161013 A161014


KEYWORD

cons,nonn


AUTHOR

Harry J. Smith, Jun 13 2009


STATUS

approved



