The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A198755 Decimal expansion of x>0 satisfying x^2+cos(x)=2. 106
 1, 3, 2, 5, 6, 2, 2, 5, 1, 8, 1, 4, 7, 5, 3, 6, 6, 2, 3, 4, 8, 3, 2, 2, 9, 0, 2, 9, 3, 8, 7, 9, 8, 7, 4, 4, 3, 3, 0, 4, 5, 4, 6, 7, 2, 5, 6, 5, 7, 6, 6, 4, 9, 5, 2, 6, 2, 7, 4, 0, 1, 8, 5, 3, 2, 0, 0, 8, 9, 5, 0, 6, 1, 6, 5, 9, 3, 0, 2, 4, 6, 5, 0, 3, 4, 1, 1, 0, 9, 7, 5, 9, 7, 7, 5, 7, 5, 6, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For many choices of a,b,c, there is a unique x>0 satisfying a*x^2+b*cos(x)=c. Guide to related sequences, with graphs included in Mathematica programs: a.... b.... c..... x 1.... 1.... 2..... A198755 1.... 1.... 3..... A198756 1.... 1.... 4..... A198757 1.... 2.... 3..... A198758 1.... 2.... 4..... A198811 1.... 3.... 3..... A198812 1.... 3.... 4..... A198813 1.... 4.... 3..... A198814 1.... 4.... 4..... A198815 1.... 1.... 0..... A125578 1... -1.... 1..... A198816 1... -1.... 2..... A198817 1... -1.... 3..... A198818 1... -1.... 4..... A198819 1... -2.... 1..... A198821 1... -2.... 2..... A198822 1... -2.... 3..... A198823 1... -2.... 4..... A198824 1... -2... -1..... A198825 1... -3.... 0..... A197807 1... -3.... 1..... A198826 1... -3.... 2..... A198828 1... -3.... 3..... A198829 1... -3.... 4..... A198830 1... -3... -1..... A198835 1... -3... -2..... A198836 1... -4.... 0..... A197808 1... -4.... 1..... A198838 1... -4.... 2..... A198839 1... -4.... 3..... A198840 1... -4.... 4..... A198841 1... -4... -1..... A198842 1... -4... -2..... A198843 1... -4... -3..... A198844 2.... 0.... 1..... A010503 2.... 0.... 3..... A115754 2.... 1.... 2..... A198820 2.... 1.... 3..... A198827 2.... 1.... 4..... A198837 2.... 2.... 3..... A198869 2.... 3.... 4..... A198870 2... -1.... 1..... A198871 2... -1.... 2..... A198872 2... -1.... 3..... A198873 2... -1.... 4..... A198874 2... -2... -1..... A198875 2... -2.... 3..... A198876 2... -3... -2..... A198877 2... -3... -1..... A198878 2... -3.... 1..... A198879 2... -3.... 2..... A198880 2... -3.... 3..... A198881 2... -3.... 4..... A198882 2... -4... -3..... A198883 2... -4... -1..... A198884 2... -4.... 1..... A198885 2... -4.... 3..... A198886 3.... 0.... 1..... A020760 3.... 1.... 2..... A198868 3.... 1.... 3..... A198917 3.... 1.... 4..... A198918 3.... 2.... 3..... A198919 3.... 2.... 4..... A198920 3.... 3.... 4..... A198921 3... -1.... 1..... A198922 3... -1.... 2..... A198924 3... -1.... 3..... A198925 3... -1.... 4..... A198926 3... -2... -1..... A198927 3... -2.... 1..... A198928 3... -2.... 2..... A198929 3... -2.... 3..... A198930 3... -2.... 4..... A198931 3... -3... -1..... A198932 3... -3.... 1..... A198933 3... -3.... 2..... A198934 3... -3.... 4..... A198935 3... -4... -3..... A198936 3... -4... -2..... A198937 3... -4... -1..... A198938 3... -4.... 1..... A198939 3... -4.... 2..... A198940 3... -4.... 3..... A198941 3... -4.... 4..... A198942 4.... 1.... 2..... A198923 4.... 1.... 3..... A198983 4.... 1.... 4..... A198984 4.... 2.... 3..... A198985 4.... 3.... 4..... A198986 4... -1.... 1..... A198987 4... -1.... 2..... A198988 4... -1.... 3..... A198989 4... -1.... 4..... A198990 4... -2... -1..... A198991 4... -2.... 1..... A198992 4... -2... -3..... A198993 4... -3... -2..... A198994 4... -3... -1..... A198995 4... -2.... 1..... A198996 4... -3.... 2..... A198997 4... -3.... 3..... A198998 4... -3.... 4..... A198999 4... -4... -3..... A199000 4... -4... -1..... A199001 4... -4.... 1..... A199002 4... -4.... 3..... A199003 Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0. We call the graph of z=g(u,v) an implicit surface of f. For an example related to A198755, take f(x,u,v)=x^2+u*cos(x)-v and g(u,v) = a nonzero solution x of f(x,u,v)=0. If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous. A portion of an implicit surface is plotted by Program 2 in the Mathematica section. LINKS Table of n, a(n) for n=1..99. EXAMPLE x=1.32562251814753662348322902938798744330... MATHEMATICA (* Program 1: A198655 *) a = 1; b = 1; c = 2; f[x_] := a*x^2 + b*Cos[x]; g[x_] := c Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}] r = x /. FindRoot[f[x] == g[x], {x, 1.32, 1.33}, WorkingPrecision -> 110] RealDigits[r] (* A198755 *) (* Program 2: implicit surface of x^2+u*cos(x)=v *) f[{x_, u_, v_}] := x^2 + u*Cos[x] - v; t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, 0, 3}]}, {u, -5, 4}, {v, u, 20}]; ListPlot3D[Flatten[t, 1]] (* for A198755 *) CROSSREFS Cf. A197737, A198414. Sequence in context: A343342 A338470 A262395 * A134237 A341521 A227192 Adjacent sequences: A198752 A198753 A198754 * A198756 A198757 A198758 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 30 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 25 11:03 EDT 2024. Contains 371967 sequences. (Running on oeis4.)