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.

User: Fabrice Auzanneau

Fabrice Auzanneau's wiki page.

Fabrice Auzanneau has authored 5 sequences.

A191896 Decimal expansion of the constant whose continued fraction is based on Padovan numbers A000931.

Original entry on oeis.org

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

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Author

Fabrice Auzanneau, Jun 18 2011

Keywords

Comments

The Padovan numbers starting at A000931(5) define a continued fraction which is converted to its floating point representation here.

Examples

			1/(1+1/(1+1/(1+1/(2+1/(2+1/(3+1/(4+1/(5+1/(7+1/(9+1/(12+1/(16+1/(21+1/(28+... = 0.630821982062263497...

Crossrefs

Cf. A000931.

Extensions

Decimals corrected by R. J. Mathar, Jul 01 2011

A191909 Decimal expansion of the limit of the square root of the ratio of consecutive Padovan numbers.

Original entry on oeis.org

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

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Author

Fabrice Auzanneau, Jun 19 2011

Keywords

Comments

This is the square root of the inverse of the plastic number A060006: 1.32471795724...
This is the positive root of x^6 + x^4 - 1 = 0 and the square root of A075778.
An algebraic integer of degree 6 and minimal polynomial x^6 + x^4 - 1. - Charles R Greathouse IV, Apr 21 2016

Examples

			0.868836961832709301806569964191...

Links

Crossrefs

Cf. A000931, A060006.

Programs

  • Mathematica
    RealDigits[x/.FindRoot[x^6+x^4==1,{x,.8},WorkingPrecision->120]][[1]] (* Harvey P. Dale, Jan 17 2014 *)
  • PARI
    polrootsreal(x^6+x^4-1)[2] \\ Charles R Greathouse IV, Apr 21 2016

A191608 Decimal expansion of number whose continued fraction is based on noncomposite numbers.

Original entry on oeis.org

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

Views

Author

Fabrice Auzanneau, Jun 08 2011

Keywords

Examples

			0.6981621154383939035335... = 1/(1+1/(2+1/(3+1/(5+1/(7+1/(11+1/(13+1/...))))))).

Formula

Equals 1/(1+A084255). - Nathaniel Johnston, Jun 08 2011
Equals 1/A152062. - R. J. Mathar, Jun 17 2011

Extensions

Corrected and extended by Nathaniel Johnston, Jun 08 2011

A191359 Continued fraction using the decimal digits of Pi.

Original entry on oeis.org

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

Views

Author

Fabrice Auzanneau, Jun 04 2011

Keywords

Examples

			0.2611882.. = 1/3.82865....

Crossrefs

Cf. A000796, A094964.

Formula

1/(3+1/(1+1/(4+1/(1+1/(5+1/(9+1/(2+1/(6+1/(5+1/(3+1/(5+1/(8+1/(9+1/(7+1/(9+1/(3+1/(2+1/...))))))))))))))))). [corrected by John M. Campbell, Aug 25 2011]
Equals 1/A094964. - R. J. Mathar, Jun 04 2011

A191504 Decimal expansion of the number 1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... )))))))))), where coefficients > 1 are the primes.

Original entry on oeis.org

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

Views

Author

Fabrice Auzanneau, Jun 04 2011

Keywords

Comments

The number can be written 1/(1+s(0)) with s(k)=prime(k)/(1+s(k+1)), prime(0):=1. Asymptotically, s(k) ~ sqrt(prime(k)).

Examples

			0.6620942517851037588123181089841636860733854770812446632320193128554043...

Crossrefs

Cf. A191608.

Programs

  • Mathematica
    N[Fold[#2/(1 + #1) &, 0, Join[Reverse@Prime@Range@180000, {1, 1}]], 111] (* Robert G. Wilson v, Jun 16 2011 *)
  • PARI
    default(realprecision,80); s=sqrt(p=1e6); while(p=precprime(p-1),s=p/(1+s)); eval(vecextract(Vec(Str((1+s)/(2+s))),"3..-2"))  \\ M. F. Hasler, Jun 16 2011

Formula

1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... ))))))))))

Extensions

Values corrected upon observation by R. J. Mathar, Jun 16 2011
Corrected and extended by Max Alekseyev, Aug 11 2013

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