A197695 - OEIS

%I #12 Oct 01 2022 00:49:53

%S 2,5,5,7,6,3,6,7,8,1,5,2,2,3,9,2,0,7,3,2,6,1,4,4,9,0,1,0,6,9,1,9,0,0,

%T 2,4,1,8,9,1,1,5,4,8,9,2,9,0,6,7,8,2,0,8,0,4,3,9,1,7,9,1,7,0,7,0,1,9,

%U 7,5,1,8,0,7,1,6,2,5,2,2,1,0,1,3,8,5,6,3,5,7,5,2,1,5,8,0,4,3,8

%N Decimal expansion of Pi/(6 + 2*Pi).

%C Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=3 and c=Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 0.255763678152239207326144901069190024189115...

%t b = 3; c = Pi;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .2, .3}]

%t N[Pi/(2*b + 2*c), 110]

%t RealDigits[%]  (* A197695 *)

%t Simplify[Pi/(2*b + 2*c)]

%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, .4}]

%t RealDigits[Pi/(6+2*Pi),10,120][[1]] (* _Harvey P. Dale_, Jun 24 2015 *)

%Y Cf. A197682.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 17 2011