A198866 -id:A198866 - cp's OEIS frontend

A199081 Decimal expansion of x > 0 satisfying x^2 + 2*sin(x) = 1.

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

Offset: 0

Clark Kimberling, Nov 02 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.7251712054289301271344240020632...
positive:  0.42302818188516042885129332473260...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A198866, A199080.

a = 1; b = 2; c = 1;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.8, -1.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A199080 *)
r = x /. FindRoot[f[x] == g[x], {x, .42, .43}, WorkingPrecision -> 110]
RealDigits[r]   (* A199081 *)

a=1; b=2; c=1; solve(x=0, 1, a*x^2 + b*sin(x) - c) \\ G. C. Greubel, Feb 20 2019

a=1; b=2; c=1; (a*x^2 + b*sin(x)==c).find_root(0,1,x) # G. C. Greubel, Feb 20 2019

Terms a(83) onward corrected by G. C. Greubel, Feb 20 2019

A199082 Decimal expansion of x < 0 satisfying x^2 + 2*sin(x) = 2.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 02 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.96188424641083489341928077977489...
positive:  0.77498081442304344595859350247040...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for transcendental numbers.

Cf. A198866, A199083.

a = 1; b = 2; c = 2;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.97, -1.96}, WorkingPrecision -> 110]
RealDigits[r](* A199082 *)
r = x /. FindRoot[f[x] == g[x], {x, .77, .78}, WorkingPrecision -> 110]
RealDigits[r](* A199083 *)

a=1; b=2; c=2; solve(x=-2, 0, a*x^2 + b*sin(x) - c) \\ G. C. Greubel, Feb 20 2019

a=1; b=2; c=2; (a*x^2 + b*sin(x)==c).find_root(-2,0,x) # G. C. Greubel, Feb 20 2019

A199083 Decimal expansion of x>0 satisfying x^2 + 2*sin(x) = 2.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 02 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.96188424641083489341928077977489...
positive:  0.774980814423043445958593502470401...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A198866, A199082.

a = 1; b = 2; c = 2;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x/.FindRoot[f[x] == g[x], {x, -1.97, -1.96}, WorkingPrecision -> 110]
RealDigits[r](* A199082 *)
r = x/.FindRoot[f[x] == g[x], {x, .77, .78}, WorkingPrecision -> 110]
RealDigits[r](* This sequence *)

a=1; b=2; c=2; solve(x=0, 1, a*x^2 + b*sin(x) - c) \\ G. C. Greubel, Feb 20 2019

a=1; b=2; c=2; (a*x^2 + b*sin(x)==c).find_root(0,1,x) # G. C. Greubel, Feb 20 2019

Terms a(90) onward corrected by G. C. Greubel, Feb 20 2019

A199150 Decimal expansion of x<0 satisfying 3*x^2+sin(x)=3.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 03 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.1415298646423925627075066056294867784...
positive:  0.86401127242790345732955031503590029470...

Index entries for transcendental numbers.

Cf. A198866.

a = 3; b = 1; c = 3;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A199150 *)
r = x /. FindRoot[f[x] == g[x], {x, .86, .87}, WorkingPrecision -> 110]
RealDigits[r]   (* A199151 *)

A199151 Decimal expansion of x>0 satisfying 3*x^2+sin(x)=3.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 03 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.1415298646423925627075066056294867784...
positive:  0.86401127242790345732955031503590029470...

Index entries for transcendental numbers.

Cf. A198866.

a = 3; b = 1; c = 3;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A199150 *)
r = x /. FindRoot[f[x] == g[x], {x, .86, .87}, WorkingPrecision -> 110]
RealDigits[r]   (* A199151 *)

A199152 Decimal expansion of x<0 satisfying 3x^2+2sin(x)=1.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 03 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -0.93194453919657480875799482221903577743...
positive:  0.33648270192335281577039493761106778144...

Index entries for transcendental numbers.

Cf. A198866.

a = 3; b = 2; c = 1;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.94, -.93}, WorkingPrecision -> 110]
RealDigits[r]  (* A199152 *)
r = x /. FindRoot[f[x] == g[x], {x, .33, .34}, WorkingPrecision -> 110]
RealDigits[r]  (* A199153 *)

A199153 Decimal expansion of x>0 satisfying 3x^2+2sin(x)=1.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 03 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -0.93194453919657480875799482221903577743...
positive:  0.336482701923352815770394937611067781443...

Index entries for transcendental numbers.

Cf. A198866.

a = 3; b = 2; c = 1;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.94, -.93}, WorkingPrecision -> 110]
RealDigits[r]  (* A199152 *)
r = x /. FindRoot[f[x] == g[x], {x, .33, .34}, WorkingPrecision -> 110]
RealDigits[r]  (* A199153 *)

A199154 Decimal expansion of x<0 satisfying 3x^2+2sin(x)=2.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 03 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.126299940993877523992867733641868507222...
positive:  0.559372170813127047765629647326548920708...

Index entries for transcendental numbers.

Cf. A198866.

a = 3; b = 2; c = 2;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.13, -1.12}, WorkingPrecision -> 110]
RealDigits[r]  (* A199154 *)
r = x /. FindRoot[f[x] == g[x], {x, .55, .56}, WorkingPrecision -> 110]
RealDigits[r]  (* A199155 *)

A199155 Decimal expansion of x>0 satisfying 3x^2+2sin(x)=2.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 03 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.126299940993877523992867733641868507222...
positive:  0.559372170813127047765629647326548920708...

Index entries for transcendental numbers.

Cf. A198866.

a = 3; b = 2; c = 2;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.13, -1.12}, WorkingPrecision -> 110]
RealDigits[r]  (* A199154 *)
r = x /. FindRoot[f[x] == g[x], {x, .55, .56}, WorkingPrecision -> 110]
RealDigits[r]  (* A199155 *)

A199156 Decimal expansion of x < 0 satisfying 3x^2+2sin(x) = 3.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 03 2011

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.280117027823592900045689845558554979655...
positive:  0.741456706769858920159460956349108949987...

Index entries for transcendental numbers.

Cf. A198866.

a = 3; b = 2; c = 3;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.29, -1.28}, WorkingPrecision -> 110]
RealDigits[r]  (* A199156 *)
r = x /. FindRoot[f[x] == g[x], {x, .74, .75}, WorkingPrecision -> 110]
RealDigits[r]  (* A199157 *)

a(93) onwards corrected by Georg Fischer, Aug 01 2021

cp's OEIS Frontend

A199081 Decimal expansion of x > 0 satisfying x^2 + 2*sin(x) = 1.

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A199082 Decimal expansion of x < 0 satisfying x^2 + 2*sin(x) = 2.

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A199083 Decimal expansion of x>0 satisfying x^2 + 2*sin(x) = 2.

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A199150 Decimal expansion of x<0 satisfying 3*x^2+sin(x)=3.

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A199151 Decimal expansion of x>0 satisfying 3*x^2+sin(x)=3.

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Mathematica

A199152 Decimal expansion of x<0 satisfying 3*x^2+2*sin(x)=1.

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Mathematica

A199153 Decimal expansion of x>0 satisfying 3*x^2+2*sin(x)=1.

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Mathematica

A199154 Decimal expansion of x<0 satisfying 3*x^2+2*sin(x)=2.

A199152 Decimal expansion of x<0 satisfying 3x^2+2sin(x)=1.

A199153 Decimal expansion of x>0 satisfying 3x^2+2sin(x)=1.

A199154 Decimal expansion of x<0 satisfying 3x^2+2sin(x)=2.

A199155 Decimal expansion of x>0 satisfying 3x^2+2sin(x)=2.

A199156 Decimal expansion of x < 0 satisfying 3x^2+2sin(x) = 3.