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.

A108088 Decimal expansion of 1/(1+1/(1+2/(1+3/(1+4/(1+5/(1+...)))))).

Original entry on oeis.org

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

Views

Author

Philippe Deléham, Jun 21 2005

Keywords

Comments

Term of Ramanujan's formula (see A059444 and A060196).

Examples

			0.6556795424187984715438712307308112833992823328704...

References

  • S. R. Finch, "Mathematical Constants", Cambridge, pp. 423-428.

Links

Crossrefs

Cf. A111129.

Programs

  • Mathematica
    RealDigits[Sqrt[Pi*E/2]*Erfc[1/Sqrt[2]], 10, 111][[1]]
  • PARI
    sqrt(Pi*exp(1)/2)*erfc(1/sqrt(2)) \\ G. C. Greubel, Feb 03 2017

Formula

Equals sqrt(Pi*e/2)*erfc(1/sqrt(2)), where erfc is the complementary error function. - Daniel Forgues, Apr 14 2011
Also equals Integral_{-infinity..infinity} (1/sqrt(2*Pi))*exp(-x^2/2)/(1+x^2) dx, where the integrand is normal PDF times Cauchy PDF. - Jean-François Alcover, Apr 28 2015

A019633 Decimal expansion of sqrt(2*Pi*e).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Dec 11 1996

Keywords

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 220.

Links

Crossrefs

Cf. A059444.

Programs

Formula

Equals 2*A059444. - Michel Marcus, May 13 2014
Equals Integral_{x>=0} exp(-log(x)^2/2) dx. - Amiram Eldar, Apr 07 2021

A059445 Continued fraction for square root of (Pi * e / 2).

Original entry on oeis.org

2, 15, 14, 1, 2, 3, 17, 1, 1, 5, 1, 30, 1, 3, 2, 1, 1, 1, 3, 3, 1, 4, 2, 9, 2, 1, 9, 1, 7, 1, 6, 1, 5, 1, 5, 3, 1, 1, 3, 1, 36, 4, 18, 2, 1, 2, 4, 1, 3, 366, 3, 1, 1, 16, 2, 1, 2, 2, 1, 3, 3, 1, 5, 2, 2, 34, 1, 2, 2, 1, 18, 1, 1, 16, 1, 1, 1, 3, 4, 7, 1, 21, 6, 5, 1, 2, 1, 11, 4, 1, 1, 14, 4, 17, 1, 1
Offset: 0

Views

Author

Robert G. Wilson v, Feb 01 2001

Keywords

Examples

			2.0663656770612464692346959... = 2 + 1/(15 + 1/(14 + 1/(1 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 27 2009

References

  • C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, Oxford and NY, 2001, page 68.

Links

Crossrefs

Cf. A059444 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[Sqrt[ \[Pi]*\[ExponentialE]/2], 100]
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(Pi*exp(1)/2)); for (n=1, 20000, write("b059445.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Jun 27 2009

Extensions

Offset changed by Andrew Howroyd, Aug 04 2024
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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