A201741 -id:A201741 - cp's OEIS frontend

A201750 Decimal expansion of the nonzero number x satisfying -x^2+1=e^x.

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

Offset: 0

Clark Kimberling, Dec 05 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			-0.7145563847430096816014491264343628875...

Index entries for transcendental numbers.

Cf. A201741.

a = -1; b = 0; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A201750 *)

A201769 Decimal expansion of the number x satisfying x^2+x=e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 05 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			x=-1.235346233464687168031015630637164701695...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 1; c = 0;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
RealDigits[r]     (* A201769 *)

A201770 Decimal expansion of the nonzero number x satisfying x^2+x+1=e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 05 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			1.793282132900761007557553363901042400...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 1; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.7, 1.8}, WorkingPrecision -> 110]
RealDigits[r]     (* A201770 *)

A201772 Decimal expansion of the number x satisfying x^2+x+4=e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 06 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			2.58555463371173779562468636302780677323083330000...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 1; c = 4;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.5, 2.6}, WorkingPrecision -> 110]
RealDigits[r]     (* A201772 *)

A201889 Decimal expansion of the number x satisfying x^2+x+5=e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 06 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			2.71287718703731960221880534853920451356941...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 1; c = 5;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.7, 2.8}, WorkingPrecision -> 110]
RealDigits[r]     (* A201889 *)

A201891 Decimal expansion of the number x satisfying x^2+2x+2=e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 06 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			x=2.674060313723560317913457264591694989622787...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 2; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.6, 2.7}, WorkingPrecision -> 110]
RealDigits[r]    (* A201891 *)

A201892 Decimal expansion of the number x satisfying x^2+2x+3=e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 06 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			x=2.79947439778638966726061606183355836832848235599...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 2; c = 3;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.7, 2.8}, WorkingPrecision -> 110]
RealDigits[r]     (* A201892 *)

A201893 Decimal expansion of the number x satisfying x^2+2x+4=e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 06 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			x=2.9034468790268968582868881770340759008300...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 2; c = 4;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]    (* A201893 *)

A201894 Decimal expansion of the number x satisfying x^2 + 2x + 5 = e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 06 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			2.9928845903382044191145349078323342337040238211311...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 2; c = 5;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]    (* A201894 *)

a(85) onwards corrected by Georg Fischer, Aug 03 2021

A201896 Decimal expansion of the greatest x satisfying x^2 + 3*x + 1 = e^x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Dec 06 2011

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

			least:  -2.649219887767292965348496137953408152796...
greatest:  2.8931164309252712203155349313495308853...

Index entries for transcendental numbers.

Cf. A201741.

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -4, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.7, -2.6}, WorkingPrecision -> 110]
RealDigits[r]     (* A201895 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]     (* A201896 *)  (* NOTE 3 zeros *)

a(98) onwards corrected by Georg Fischer, Aug 03 2021

cp's OEIS Frontend

A201750 Decimal expansion of the nonzero number x satisfying -x^2+1=e^x.

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A201769 Decimal expansion of the number x satisfying x^2+x=e^x.

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A201770 Decimal expansion of the nonzero number x satisfying x^2+x+1=e^x.

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A201772 Decimal expansion of the number x satisfying x^2+x+4=e^x.

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A201889 Decimal expansion of the number x satisfying x^2+x+5=e^x.

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Mathematica

A201891 Decimal expansion of the number x satisfying x^2+2x+2=e^x.

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Mathematica

A201892 Decimal expansion of the number x satisfying x^2+2x+3=e^x.

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Mathematica

A201893 Decimal expansion of the number x satisfying x^2+2x+4=e^x.

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