A201397 -id:A201397 - cp's OEIS frontend

A201516 Decimal expansion of greatest x satisfying 3*x^2 - 1 = sec(x) and 0 < x < Pi.

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

Offset: 1

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.95353909754991468966727069537237822743...
greatest: 1.341430166291259764576080506763614171...

Index entries for transcendental numbers.

Cf. A201397.

a = 3; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .9, 1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201515 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A201516 *)

A201517 Decimal expansion of least x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.774427257079893623257029009000...
greatest: 1.4313635500690391357640449937...

Index entries for transcendental numbers.

Cf. A201397.

a = 4; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
RealDigits[r]   (* A201517 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201518 *)

A201518 Decimal expansion of greatest x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.774427257079893623257029009000...
greatest: 1.4313635500690391357640449937...

Index entries for transcendental numbers.

Cf. A201397.

a = 4; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
RealDigits[r]   (* A201517 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201518 *)

A201519 Decimal expansion of least x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.675482908113724228015178858190...
greatest: 1.4683742920332829376554687815...

Index entries for transcendental numbers.

Cf. A201397.

a = 5; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]   (* A201519 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201520 *)

A201520 Decimal expansion of greatest x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least: 0.675482908113724228015178858190...
greatest: 1.4683742920332829376554687815...

Index entries for transcendental numbers.

Cf. A201397.

a = 5; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]   (* A201519 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201520 *)

A201521 Decimal expansion of least x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.60805447799791305332799572251089761...
greatest: 1.489480656731833320399126017677317...

Index entries for transcendental numbers.

Cf. A201397.

a = 6; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]   (* A201521 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201522 *)

A201522 Decimal expansion of greatest x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.60805447799791305332799572251089761...
greatest: 1.489480656731833320399126017677317...

Index entries for transcendental numbers.

Cf. A201397.

a = 6; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]   (* A201521 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201522 *)

A201523 Decimal expansion of least x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.557895175779035299832869736313873...
greatest: 1.5032621521314930999190799075200...

Index entries for transcendental numbers.

Cf. A201397.

a = 7; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201523 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201524 *)

A201524 Decimal expansion of greatest x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.557895175779035299832869736313873...
greatest: 1.5032621521314930999190799075200...

Index entries for transcendental numbers.

Cf. A201397.

a = 7; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201523 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201524 *)

A201525 Decimal expansion of least x satisfying 8*x^2 - 1 = sec(x) and 0 < x < Pi.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Dec 02 2011

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

			least:  0.518577002201711458253109820417244...
greatest: 1.5130057374477490977746930540120...

Index entries for transcendental numbers.

Cf. A201397.

a = 8; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201525 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201526 *)

cp's OEIS Frontend

A201516 Decimal expansion of greatest x satisfying 3*x^2 - 1 = sec(x) and 0 < x < Pi.

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A201517 Decimal expansion of least x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

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A201518 Decimal expansion of greatest x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

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A201519 Decimal expansion of least x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

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A201520 Decimal expansion of greatest x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

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A201521 Decimal expansion of least x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.

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A201522 Decimal expansion of greatest x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.

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Mathematica

A201523 Decimal expansion of least x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.

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