A201564 -id:A201564 - cp's OEIS frontend

A201589 Decimal expansion of least x satisfying 5*x^2 = csc(x) and 0 < x < Pi.

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

Offset: 0

Clark Kimberling, Dec 03 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.596626819860704546761832859082141048303653100...
greatest:  3.121059463523827415360175700034092048910749...

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

Cf. A201564.

a = 5; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201589 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201590 *)

a=5; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Terms a(90) onward corrected by G. C. Greubel, Aug 22 2018

A201590 Decimal expansion of greatest x satisfying 5*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 03 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.596626819860704546761832859082141048303653100...
greatest:  3.121059463523827415360175700034092048910749...

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

Cf. A201564.

a = 5; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201589 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201590 *)

a=5; c=0; solve(x=3.1, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Terms a(88) onward corrected by G. C. Greubel, Aug 22 2018

A201591 Decimal expansion of least x satisfying 6*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 03 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.56010069491216076282384133379781207752937450...
greatest:  3.12451991250138769396880196501162499414487...

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

Cf. A201564.

a = 6; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201591 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201653 *)

a=6; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Terms a(90) onward corrected by G. C. Greubel, Aug 22 2018

A201653 Decimal expansion of greatest x satisfying 6*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 03 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.56010069491216076282384133379781207752937450...
greatest:  3.12451991250138769396880196501162499414487...

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

Cf. A201564.

a = 6; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201591 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201653 *)

a=6; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

A201654 Decimal expansion of least x satisfying 7*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 04 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.53109378322877556954245426287272878812709738...
greatest:  3.12698210171419101601393999273016371798979...

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

Cf. A201564.

a = 7; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201654 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201655 *)

a=7; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

A201655 Decimal expansion of greatest x satisfying 7*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 04 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.53109378322877556954245426287272878812709738...
greatest:  3.12698210171419101601393999273016371798979...

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

Cf. A201564.

a = 7; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201654 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201655 *)

a=7; c=0; solve(x=3.1, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

A201656 Decimal expansion of least x satisfying 8*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 04 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.507262199349103778265812147726404197638586...
greatest:  3.128823571901654937275752484725028832935...

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

Cf. A201564.

a = 8; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201656 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201657 *)

a=8; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

A201657 Decimal expansion of greatest x satisfying 8*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 04 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.507262199349103778265812147726404197638586...
greatest:  3.128823571901654937275752484725028832935...

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

Cf. A201564.

a = 8; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201656 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201657 *)

a=8; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 23 2018

A201658 Decimal expansion of least x satisfying 9*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 04 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.4871825725461343607675424300430642207826...
greatest:  3.1302527861735360350037012277754031636...

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

Cf. A201564.

a = 9; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]    (* A201658 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]    (* A201659 *)

a=9; c=0; solve(x=.4, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018

Terms a(89) onward corrected by G. C. Greubel, Sep 11 2018

A201659 Decimal expansion of greatest x satisfying 9*x^2 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 04 2011

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.4871825725461343607675424300430642207826...
greatest:  3.1302527861735360350037012277754031636...

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

Cf. A201564.

a = 9; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]    (* A201658 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]    (* A201659 *)

a=9; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018

cp's OEIS Frontend

A201589 Decimal expansion of least x satisfying 5*x^2 = csc(x) and 0 < x < Pi.

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A201590 Decimal expansion of greatest x satisfying 5*x^2 = csc(x) and 0 < x < Pi.

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A201591 Decimal expansion of least x satisfying 6*x^2 = csc(x) and 0 < x < Pi.

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Extensions

A201653 Decimal expansion of greatest x satisfying 6*x^2 = csc(x) and 0 < x < Pi.

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Mathematica

PARI

A201654 Decimal expansion of least x satisfying 7*x^2 = csc(x) and 0 < x < Pi.

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Mathematica

PARI

A201655 Decimal expansion of greatest x satisfying 7*x^2 = csc(x) and 0 < x < Pi.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A201656 Decimal expansion of least x satisfying 8*x^2 = csc(x) and 0 < x < Pi.

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Mathematica