A199597 -id:A199597 - cp's OEIS frontend

A199612 Decimal expansion of greatest x satisfying x + 4*cos(x) = 0.

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

Offset: 1

Clark Kimberling, Nov 08 2011

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

			least: -1.25235323400258876318632812197538043590128...
greatest:  3.595304867161547991877606935083418714913111...

Index entries for transcendental numbers.

Cf. A199597, A199611.

a = 1; b = 4; c = 0;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A199611, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199612, greatest of 4 roots *)

a(86) onwards corrected by Georg Fischer, Aug 03 2021

A199613 Decimal expansion of least x satisfying x^2+4xcos(x)=sin(x) (negated).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 08 2011

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

			least: -1.077309917524072030339979615126813664791...
greatest: 3.553241680682892523957265556234494902067...

Iain Fox, Table of n, a(n) for n = 1..20000
Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
RealDigits[r]  (* A199613, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199614, greatest of 4 roots *)

solve(x=-2, -1, x^2+4*x*cos(x)-sin(x)) \\ Iain Fox, Nov 22 2017

A199614 Decimal expansion of greatest x satisfying x^2+4xcos(x)=sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 08 2011

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

			least: -1.077309917524072030339979615126813664791...
greatest:  3.553241680682892523957265556234494902...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
RealDigits[r]  (* A199613, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199614, greatest of 4 roots *)

A199615 Decimal expansion of least x satisfying x^2 + 4xcos(x) = 2*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 08 2011

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

			least: -0.856374049744346109322078062564729199476600...
greatest:  3.515613199687358023842180210704030792217...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.86, -.85}, WorkingPrecision -> 110]
RealDigits[r]  (* A199615, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199616, greatest of 4 roots *)

a(96) onwards corrected by Georg Fischer, Aug 03 2021

A199616 Decimal expansion of greatest x satisfying x^2+4xcos(x)=2*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 08 2011

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

			least: -0.856374049744346109322078062564729199476600...
greatest:  3.515613199687358023842180210704030792217...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.86, -.85}, WorkingPrecision -> 110]
RealDigits[r]  (* A199615, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199616, greatest of 4 roots *)

A199617 Decimal expansion of least x satisfying x^2+4xcos(x)=3*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 08 2011

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

			least: -0.5535433817860336287020344905911816930...
greatest:  3.4822676247861932090867036675576803...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.56, -.55}, WorkingPrecision -> 110]
RealDigits[r]  (* A199617, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199618, greatest of 4 roots *)

A199618 Decimal expansion of greatest x satisfying x^2+4xcos(x)=3*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 08 2011

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

			least: -0.5535433817860336287020344905911816930...
greatest:  3.4822676247861932090867036675576803...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.56, -.55}, WorkingPrecision -> 110]
RealDigits[r]  (* A199617, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199618, greatest of 4 roots *)

A199619 Decimal expansion of least x>0 satisfying x^2+4xcos(x)=4*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 08 2011

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

			least: 0.80005334262741575936859027990893321963...
greatest:  3.4528998885329277803363008378649838...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.5, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .8, .81}, WorkingPrecision -> 110]
RealDigits[r]  (* A199619, least pos root *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199620, greatest of 3 roots *)

A199620 Decimal expansion of greatest x satisfying x^2+4xcos(x)=4*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 08 2011

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

			least: 0.80005334262741575936859027990893321963...
greatest:  3.4528998885329277803363008378649838...

Index entries for transcendental numbers.

Cf. A199597.

a = 1; b = 4; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.5, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .8, .81}, WorkingPrecision -> 110]
RealDigits[r]  (* A199619, least pos root *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199620, greatest of 3 roots *)

A199661 Decimal expansion of x>0 satisfying 2x^2+2xcos(x)=3sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 09 2011

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

			0.5811482272034121119867976746206496441856...

Index entries for transcendental numbers.

Cf. A199597.

a = 2; b = 2; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
RealDigits[r]  (* A199661 *)

cp's OEIS Frontend

A199612 Decimal expansion of greatest x satisfying x + 4*cos(x) = 0.

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A199613 Decimal expansion of least x satisfying x^2+4*x*cos(x)=sin(x) (negated).

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A199614 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=sin(x).

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A199615 Decimal expansion of least x satisfying x^2 + 4*x*cos(x) = 2*sin(x).

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A199616 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=2*sin(x).

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A199617 Decimal expansion of least x satisfying x^2+4*x*cos(x)=3*sin(x).

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A199618 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=3*sin(x).

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A199619 Decimal expansion of least x>0 satisfying x^2+4*x*cos(x)=4*sin(x).

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A199613 Decimal expansion of least x satisfying x^2+4xcos(x)=sin(x) (negated).

A199614 Decimal expansion of greatest x satisfying x^2+4xcos(x)=sin(x).

A199615 Decimal expansion of least x satisfying x^2 + 4xcos(x) = 2*sin(x).

A199616 Decimal expansion of greatest x satisfying x^2+4xcos(x)=2*sin(x).

A199617 Decimal expansion of least x satisfying x^2+4xcos(x)=3*sin(x).

A199618 Decimal expansion of greatest x satisfying x^2+4xcos(x)=3*sin(x).

A199619 Decimal expansion of least x>0 satisfying x^2+4xcos(x)=4*sin(x).

A199620 Decimal expansion of greatest x satisfying x^2+4xcos(x)=4*sin(x).

A199661 Decimal expansion of x>0 satisfying 2x^2+2xcos(x)=3sin(x).