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.

Showing 1-3 of 3 results.

A100944 Continued fraction of constant in A100943: positive solution of y^2-y-e=0.

Original entry on oeis.org

2, 4, 2, 18, 1, 1, 1, 1, 4, 1, 6, 1, 6, 4, 5, 3, 1, 1, 1, 2, 7, 1, 2, 1, 2, 3, 1, 8, 5, 243, 8, 1, 5, 6, 1, 7, 3, 12, 1, 5, 1, 90, 82, 2, 2, 3, 2, 2, 2, 3, 2, 16, 3, 1, 3, 26, 277, 2, 1, 1, 2, 1, 2, 1, 4, 4, 2, 36, 2, 2, 1, 1, 92, 1, 20, 3, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 5, 25, 2, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 2, 1, 1, 6, 1, 5, 69, 1, 1, 1, 1, 1, 1, 1, 3, 6, 4, 3, 1, 1
Offset: 0

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 23 2004

Keywords

Crossrefs

Cf. A100943.

Programs

  • Mathematica
    ContinuedFraction[(1+Sqrt[1+4E])/2,120] (* Harvey P. Dale, Jan 08 2019 *)

Formula

(1+sqrt(1+4*e))/2

Extensions

Corrected and extended by Harvey P. Dale, Jan 08 2019

A275828 Decimal expansion of the nested surd sqrt(phi + sqrt(phi + sqrt(phi + sqrt(phi + ... )))) where phi is golden ratio = (1 + sqrt(5))/2; see A001622.

Original entry on oeis.org

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

Views

Author

Jaroslav Krizek, Aug 10 2016

Keywords

Comments

Also decimal expansion of (1 + (sqrt(1 + 4*((1 + sqrt(5)) / 2)))) / 2.
Sequence with a(1) = 0 is decimal expansion of the nested surd sqrt(phi - sqrt(phi - sqrt(phi - sqrt(phi - ...)))) where phi is golden ratio = (1 + sqrt(5))/2; see A001622.
Solution of y^2 - y - phi = 0.

Examples

			1.866760399173862092990872...

Links

Crossrefs

Cf. A001622, A100943, A100941, Cf. A298522.

Programs

  • Mathematica
    u = N[(1/2) (1 + Sqrt[3 + 2*Sqrt[5]]), 100]
RealDigits[u][[1]] (* Clark Kimberling, Jan 25 2018 *)

Formula

Equals (1/2)*(1+sqrt(3+2*sqrt(5))). - Clark Kimberling, Jan 25 2018

Extensions

Terms corrected by Clark Kimberling, Jan 25 2018

A271529 Decimal expansion of sqrt(e + e*sqrt(e + e*sqrt(e + ...))).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 09 2016

Keywords

Examples

			3.495854711908497636885040848013394528609516258957759538...

Links

  • Eric Weisstein's World of Mathematics, e
  • Eric Weisstein's World of Mathematics, Nested Radical

Crossrefs

Cf. A001113, A019774, A100943, A189970, A268580.

Programs

  • Mathematica
    RealDigits[Sqrt[E] ((Sqrt[E] + Sqrt[E + 4])/2), 10, 120][[1]]
  • PARI
    exp(1)/2+sqrt(4*exp(1)+exp(2))/2 \\ Charles R Greathouse IV, Apr 20 2016
  • PARI
    t=exp(.5); t*(t+sqrt(exp(1)+4))/2 \\ Charles R Greathouse IV, Apr 20 2016

Formula

Equals sqrt(e)*(sqrt(e) + sqrt(e + 4))/2.
Equals e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/...))))))))).
Showing 1-3 of 3 results.

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