cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A197134 Decimal expansion of least x>0 having sin(x)=(sin 3x)^2.

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%I A197134 #13 Feb 12 2025 16:09:42
%S A197134 1,1,5,4,0,2,2,6,7,3,8,7,1,2,7,8,8,2,8,5,9,2,3,6,7,4,7,9,5,7,3,6,8,7,
%T A197134 0,4,8,4,0,3,5,4,2,1,9,7,7,9,8,2,0,1,9,0,3,3,3,9,1,1,7,8,6,8,2,4,2,8,
%U A197134 6,9,2,2,4,2,3,8,9,4,6,1,7,7,3,0,4,8,6,3,1,4,6,1,2,8,4,3,4,5,5,6
%N A197134 Decimal expansion of least x>0 having sin(x)=(sin 3x)^2.
%C A197134 The Mathematica program includes a graph.  See A197133 for a guide to least x>0 satisfying sin(b*x)=(sin(c*x))^2 for selected b and c.
%H A197134 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A197134 0.115402267387127882859236747957368...
%t A197134 b = 1; c = 3; f[x_] := Sin[x]
%t A197134 t = x /.  FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision -> 100]
%t A197134 RealDigits[t] (* A197134 *)
%t A197134 Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
%t A197134 RealDigits[ ArcCos[ Root[ 17 - 112 #^2 + 352 #^4 - 512 #^6 + 256 #^8 &, 4]], 10, 100] // First (* _Jean-François Alcover_, Feb 19 2013 *)
%o A197134 (PARI) acos(polrootsreal(256*x^8-512*x^6+352*x^4-112*x^2+17)[4]) \\ _Charles R Greathouse IV_, Feb 12 2025
%Y A197134 Cf. A197133.
%K A197134 nonn,cons
%O A197134 0,3
%A A197134 _Clark Kimberling_, Oct 12 2011
%E A197134 Digits from a(79) on corrected by _Jean-François Alcover_, Feb 19 2013