A201564 -id:A201564 - cp's OEIS frontend

A201568 Decimal expansion of least x satisfying x^2 + 4 = csc(x) and 0 < x < Pi.

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

Offset: 0

Clark Kimberling, Dec 03 2011

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

			least:  0.2487490007162959853652924083716941039...
greatest:  3.0669301776557967159210627137381980...

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

Cf. A201564.

a = 1; c = 4;
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, .2, .3}, WorkingPrecision -> 110]
RealDigits[r]   (* A201568 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201569 *)

a=1; c=4; solve(x=0.2, .3, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

A201578 Decimal expansion of least x satisfying x^2 + 10 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 03 2011

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

			least:  0.100066884072919309279805384459381115060...
greatest:  3.090421270152151453651497443899920534...

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

Cf. A201564.

a = 1; c = 10;
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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201578 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201581 *)

a=1; c=10; solve(x=0.1, 0.2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

A201567 Decimal expansion of greatest x satisfying x^2 + 3 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 03 2011

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

			least:  0.3276482471136686780982477062098195298...
greatest:  3.0606476216743906494670210614415753...

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

Cf. A201564.

a = 1; c = 3;
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, .3, .4}, WorkingPrecision -> 110]
RealDigits[r]    (* A201567 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201568 *)

a=1; c=3; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

A201569 Decimal expansion of greatest x satisfying x^2 + 4 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 03 2011

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

			least:  0.2487490007162959853652924083716941039...
greatest:  3.0669301776557967159210627137381980...

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

Cf. A201564.

a = 1; c = 4;
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, .2, .3}, WorkingPrecision -> 110]
RealDigits[r]   (* A201568 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201569 *)

a=1; c=4; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

A201570 Decimal expansion of least x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 03 2011

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

			least:  0.19974229281947213708674051595534811453...
greatest:  3.07227983005125033585986646046469906...

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

Cf. A201564.

a = 1; c = 5;
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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201570 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201571 *)

a=1; c=5; solve(x=0.1, 0.2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

A201571 Decimal expansion of greatest x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 03 2011

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

			least:  0.19974229281947213708674051595534811453...
greatest:  3.07227983005125033585986646046469906...

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

Cf. A201564.

a = 1; c = 5;
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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201570 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201571 *)

a=1; c=5; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

A201572 Decimal expansion of least x satisfying x^2 + 6 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 03 2011

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

			least:  0.166669163175400949565200320627761299158167...
greatest:  3.076894929246192023166693647327725773248...

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

Cf. A201564.

a = 1; c = 6;
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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201572 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201573 *)

a=1; c=6; solve(x=0.1, .2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

Terms a(83) onward corrected by G. C. Greubel, Aug 21 2018

A201573 Decimal expansion of greatest x satisfying x^2 + 6 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 03 2011

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

			least:  0.166669163175400949565200320627761299158167...
greatest:  3.076894929246192023166693647327725773248...

Index entries for transcendental numbers.

Cf. A201564.

a = 1; c = 6;
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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201572 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201573 *)

a=1; c=6; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

Terms a(87) onward corrected by G. C. Greubel, Aug 21 2018

A201574 Decimal expansion of least x satisfying x^2 + 7 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 03 2011

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

			least:  0.14292758299392086700431044307554748240884...
greatest:  3.08092023229520680455935849821275370108...

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

Cf. A201564.

a = 1; c = 7;
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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201574 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201575 *)

a=1; c=7; solve(x=0.1, .2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

A201575 Decimal expansion of greatest x satisfying x^2 + 7 = csc(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 03 2011

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

			least:  0.14292758299392086700431044307554748240884...
greatest:  3.08092023229520680455935849821275370108...

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

Cf. A201564.

a = 1; c = 7;
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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201574 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201575 *)

a=1; c=7; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

cp's OEIS Frontend

A201568 Decimal expansion of least x satisfying x^2 + 4 = csc(x) and 0 < x < Pi.

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A201578 Decimal expansion of least x satisfying x^2 + 10 = csc(x) and 0 < x < Pi.

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A201567 Decimal expansion of greatest x satisfying x^2 + 3 = csc(x) and 0 < x < Pi.

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A201569 Decimal expansion of greatest x satisfying x^2 + 4 = csc(x) and 0 < x < Pi.

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A201570 Decimal expansion of least x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.

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A201571 Decimal expansion of greatest x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.

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Mathematica

PARI

A201572 Decimal expansion of least x satisfying x^2 + 6 = csc(x) and 0 < x < Pi.

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A201573 Decimal expansion of greatest x satisfying x^2 + 6 = csc(x) and 0 < x < Pi.