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A197690
Decimal expansion of Pi/(4 + 2*Pi).
2
3, 0, 5, 5, 0, 7, 7, 3, 5, 1, 7, 5, 8, 2, 8, 6, 4, 4, 6, 9, 0, 2, 9, 7, 6, 9, 3, 9, 7, 6, 9, 8, 4, 4, 3, 0, 8, 6, 8, 7, 1, 1, 3, 1, 6, 4, 7, 8, 0, 4, 6, 3, 9, 7, 6, 0, 4, 4, 5, 8, 3, 8, 7, 5, 2, 1, 2, 3, 2, 4, 1, 6, 9, 6, 8, 1, 5, 7, 9, 1, 9, 3, 2, 8, 6, 8, 5, 6, 9, 1, 7, 2, 8, 3, 3, 7, 1, 5, 2
OFFSET
0,1
COMMENTS
Least x > 0 such that sin(b*x)=cos(c*x) (and also sin(c*x)=cos(b*x)), where b=2 and c=Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.
EXAMPLE
0.30550773517582864469029769397698443086...
MATHEMATICA
b = 2; c = Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .3, .31}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%] (* A197690 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
CROSSREFS
Cf. A197682.
Sequence in context: A021770 A004589 A354836 * A351692 A181840 A198432
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 17 2011
STATUS
approved