A199597 -id:A199597 - cp's OEIS frontend

A199723 Decimal expansion of x>0 satisfying x^2-2xcos(x)=4*sin(x).

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.780608119966635204337801849076666...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -2; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.78, 1.79}, WorkingPrecision -> 110]
RealDigits[r]  (* A199723 *)

A199724 Decimal expansion of x>0 satisfying x^2-2xcos(x)=3*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.651000934439715798306848089804572814415828...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -2; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.65, 1.66}, WorkingPrecision -> 110]
RealDigits[r]   (* A199724 *)

A199725 Decimal expansion of x>0 satisfying x^2-2xcos(x)=2*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.4924632398063786720704065895280437990...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -2; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.49, 1.50}, WorkingPrecision -> 110]
RealDigits[r]  (* A199725 *)

A199726 Decimal expansion of x>0 satisfying x^2-2xcos(x)=sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.29276238477349584606788843541577942175797443...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -2; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.29, 1.30}, WorkingPrecision -> 110]
RealDigits[r]  (* A199726 *)

A199727 Decimal expansion of x>0 satisfying x^2-3xcos(x)=4*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.7436889564913023161629215530136008534044...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -3; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.74, 1.75}, WorkingPrecision -> 110]
RealDigits[r]    (* A199727 *)

A199728 Decimal expansion of x>0 satisfying x^2-3xcos(x)=3*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.635688751154110179778614418037790948409...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -3; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.63, 1.64}, WorkingPrecision -> 110]
RealDigits[r]    (* A199728 *)

A199729 Decimal expansion of x>0 satisfying x^2-3xcos(x)=2*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.50881670334950305078101808272216340439160111...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -3; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.50, 1.51}, WorkingPrecision -> 110]
RealDigits[r]    (* A199729 *)

A199730 Decimal expansion of x>0 satisfying x^2-3xcos(x)=sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 09 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.3569200623613718442251034863373965462473491...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = -3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.35, 1.36}, WorkingPrecision -> 110]
RealDigits[r]   (* A199730 *)

A199739 Decimal expansion of x>0 satisfying 2x^2-xcos(x)=4*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 10 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.44098516321037377845138045423482842700444...

Matthew House, Table of n, a(n) for n = 1..10000
Index entries for transcendental numbers.

Cf. A199597.

a = 2; b = -1; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.44, 1.45}, WorkingPrecision -> 110]
RealDigits[r]   (* A199739 *)

Definition corrected by Matthew House, Dec 24 2016

A199740 Decimal expansion of x>0 satisfying 2x^2-xcos(x)=3*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 10 2011

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

			1.27308071490101535925027278315193189066832...

Index entries for transcendental numbers.

Cf. A199597.

a = 2; b = -1; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.27, 1.28}, WorkingPrecision -> 110]
RealDigits[r]   (* A199740 *)

Name corrected by Sean A. Irvine, Jan 12 2025

cp's OEIS Frontend

A199723 Decimal expansion of x>0 satisfying x^2-2*x*cos(x)=4*sin(x).

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A199724 Decimal expansion of x>0 satisfying x^2-2*x*cos(x)=3*sin(x).

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A199725 Decimal expansion of x>0 satisfying x^2-2*x*cos(x)=2*sin(x).

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A199726 Decimal expansion of x>0 satisfying x^2-2*x*cos(x)=sin(x).

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A199727 Decimal expansion of x>0 satisfying x^2-3*x*cos(x)=4*sin(x).

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A199728 Decimal expansion of x>0 satisfying x^2-3*x*cos(x)=3*sin(x).

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Mathematica

A199729 Decimal expansion of x>0 satisfying x^2-3*x*cos(x)=2*sin(x).

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Mathematica

A199730 Decimal expansion of x>0 satisfying x^2-3*x*cos(x)=sin(x).

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A199723 Decimal expansion of x>0 satisfying x^2-2xcos(x)=4*sin(x).

A199724 Decimal expansion of x>0 satisfying x^2-2xcos(x)=3*sin(x).

A199725 Decimal expansion of x>0 satisfying x^2-2xcos(x)=2*sin(x).

A199726 Decimal expansion of x>0 satisfying x^2-2xcos(x)=sin(x).

A199727 Decimal expansion of x>0 satisfying x^2-3xcos(x)=4*sin(x).

A199728 Decimal expansion of x>0 satisfying x^2-3xcos(x)=3*sin(x).

A199729 Decimal expansion of x>0 satisfying x^2-3xcos(x)=2*sin(x).

A199730 Decimal expansion of x>0 satisfying x^2-3xcos(x)=sin(x).

A199739 Decimal expansion of x>0 satisfying 2x^2-xcos(x)=4*sin(x).

A199740 Decimal expansion of x>0 satisfying 2x^2-xcos(x)=3*sin(x).