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 1-4 of 4 results.

A329304 Numerators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, ...].

Original entry on oeis.org

0, 1, 8, 217, 13896, 1737217, 375252768, 128713436641, 65901654812960, 48042435072084481, 48042500973739293960, 63944616838482072345241, 110496345939397994751870408, 242760535973474232951931631617, 666135021207559234618095149027456
Offset: 0

Views

Author

Jianing Song, Nov 30 2019

Keywords

Examples

			Convergents to [0; 1, 8, 27, 64, ...]: 0, 1, 8/9, 217/244, 13896/15625, 1737217/1953369, 375252768/421943329, ...

Links

Crossrefs

Cf. A309930, A329305 (denominators), A001053, A036245.

Programs

  • PARI
    A329304_up_to_n(n) = my(v=vector(n+1)); for(i=1, n+1, if(i==1, v[i]=0, if(i==2, v[i]=1, v[i]=(i-1)^3*v[i-1]+v[i-2]))); v

Formula

a(0) = 0, a(1) = 1, a(n) = n^3*a(n-1) + a(n-2) for n >= 2.

A329305 Denominators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, ...].

Original entry on oeis.org

1, 1, 9, 244, 15625, 1953369, 421943329, 144728515216, 74101421733921, 54020081172543625, 54020155273965358921, 71900880689729065267476, 124244775852007098747557449, 272965844447740285677448982929, 749018401409375195906018756714625
Offset: 0

Views

Author

Jianing Song, Nov 30 2019

Keywords

Examples

			Convergents to [0; 1, 8, 27, 64, ...]: 0, 1, 8/9, 217/244, 13896/15625, 1737217/1953369, 375252768/421943329, ...

Links

Crossrefs

Cf. A309930, A329304 (numerators), A001040, A036246.

Programs

  • PARI
    A329305_up_to_n(n) = my(v=vector(n+1)); for(i=1, n+1, if(i==1, v[i]=1, if(i==2, v[i]=1, v[i]=(i-1)^3*v[i-1]+v[i-2]))); v

Formula

a(0) = 1, a(1) = 1, a(n) = n^3*a(n-1) + a(n-2) for n >= 2.

A073824 Decimal expansion of number with continued fraction expansion 0, 1, 4, 9, ... (the squares).

Original entry on oeis.org

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

Views

Author

Rick L. Shepherd, Aug 12 2002

Keywords

Examples

			0.80431856111715795076768044139...

Links

Crossrefs

Cf. A000290 (squares), A052119, A309930, A214070.
The numerators and denominators of convergents to this constant are given by A036245 and A036246 respectively.

Programs

  • Mathematica
    RealDigits[FromContinuedFraction[Range[0,100]^2],10,120][[1]] (* Harvey P. Dale, May 07 2018 *)
  • PARI
    dec_exp(v)= w=contfracpnqn(v); w[1,1]/w[2,1]+0.
dec_exp(vector(2000,i,(i-1)^2))

A214070 Decimal expansion of the number whose continued fraction is 1, 2, 4, 8, 16, ...

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Aug 06 2012

Keywords

Comments

Essentially the same as A096641. - R. J. Mathar, Aug 10 2012

Examples

			1.4459346405122026681195543406826176842704088452034385079032635605006619006916...

Crossrefs

Cf. A000079, A096641, A275614.
Cf. A052119, A073824, A309930.

Programs

  • Mathematica
    RealDigits[ FromContinuedFraction[{1, 2^Range@ 19}], 10, 111][[1]]

Formula

From Amiram Eldar, Feb 08 2022: (Start)
Equals A096641 + 1.
Equals 1/A275614. (End)
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.