cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A202346 Decimal expansion of x > 0 satisfying 2*x + 2 = exp(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Dec 17 2011

Keywords

Comments

See A202320 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x<0:  -0.76803904701346556525568352607754...
x>0:  1.6783469900166606534128845120945230...

Links

Crossrefs

Cf. A202320.

Programs

  • Mathematica
    u = 2; v = 2;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]  (* A202345 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[r] (* A202346 *)
RealDigits[-1 - LambertW[-1, -Exp[-1]/2], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)
  • PARI
    solve(x=0, 2, 2*x+2-exp(x)) \\ Michel Marcus, Nov 09 2017

A202347 Decimal expansion of x < 0 satisfying x + e = exp(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Dec 17 2011

Keywords

Comments

See A202320 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x < 0: -2.64745024204996672072720122214641524...
x > 0: 1.420370118020083458458421283899772980...

Links

Crossrefs

Cf. A202320.

Programs

  • Mathematica
    u = 1; v = E;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.7, -2.6}, WorkingPrecision -> 110]
RealDigits[r] (* A202347 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A104689 *)
RealDigits[-E - LambertW[-Exp[-E]], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)
  • PARI
    solve(x=-3, 0, exp(x)-exp(1)-x) \\ Michel Marcus, Nov 09 2017

Formula

Equals -exp(1) - LambertW(-exp(-exp(1))). - G. C. Greubel, Nov 09 2017

A202344 Decimal expansion of x > 0 satisfying 3*x + 1 = exp(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Dec 17 2011

Keywords

Comments

See A202320 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x = 1.9038136944403834847101403608281351272...

Links

Crossrefs

Cf. A202320.

Programs

  • Mathematica
    u = 3; v = 1;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.9, 2.0}, WorkingPrecision -> 110]
RealDigits[r]  (* A202344 *)
RealDigits[-1/3 - ProductLog[-1, -1/(3*E^(1/3))], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)
  • PARI
    solve(x=1, 2, 3*x+1-exp(x)) \\ Michel Marcus, Nov 09 2017

A202350 Decimal expansion of x > 0 satisfying e*x + 1 = exp(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Dec 17 2011

Keywords

Comments

See A202320 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			1.750786722680146367570014877255332...

Links

Crossrefs

Cf. A001113, A202320.

Programs

  • Mathematica
    u = E; v = 1;
f[x_] := u*x + v; 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]  (* A202350 *)
(* alternate program *)
RealDigits[(-1 - E*ProductLog[-1, -E^(-1-1/E)])/E, 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

Formula

Equals -LambertW(-1, -1/exp(1+1/e)) - 1/e. - Andrea Pinos, Sep 12 2023
Previous Showing 11-14 of 14 results.

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