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.

A196767 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/2), or, equivalently, -1 = x*cos(x).

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%I A196767 #13 Feb 11 2025 13:52:53
%S A196767 2,0,7,3,9,3,2,8,0,9,0,9,1,2,1,4,9,0,1,1,6,7,7,7,6,2,9,7,7,9,9,3,6,0,
%T A196767 0,6,7,9,4,6,2,1,9,5,3,1,5,2,8,5,3,0,5,4,4,6,7,9,2,9,5,2,6,7,8,5,7,8,
%U A196767 6,8,5,6,8,8,8,6,8,7,0,2,3,2,9,9,2,8,2,1,8,4,1,3,0,6,9,9,4,6,0,2,9
%N A196767 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/2), or, equivalently, -1 = x*cos(x).
%H A196767 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196767 2.073932809091214901167776297799360067946219531...
%t A196767 Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
%t A196767   0, 2 Pi}]
%t A196767 t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
%t A196767 RealDigits[t]  (* A133866 *)
%t A196767 t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
%t A196767 RealDigits[t]     (* A196767 *)
%t A196767 t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
%t A196767 RealDigits[t]   (* A196768 *)
%t A196767 t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
%t A196767 RealDigits[t]    (* A196769 *)
%t A196767 t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
%t A196767 RealDigits[t]   (* A196770 *)
%t A196767 t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
%t A196767 RealDigits[t]    (* A196771 *)
%o A196767 (PARI) solve(x=2,3, x*cos(x)+1) \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A196767 Cf. A196772.
%K A196767 nonn,cons
%O A196767 1,1
%A A196767 _Clark Kimberling_, Oct 06 2011