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 1-2 of 2 results.

A160386 Decimal expansion of Sum_{n>=0}(-1)^n/3^(2^n).

Original entry on oeis.org

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

Views

Author

Harry J. Smith, May 12 2009

Keywords

Comments

This sum is among forms which Kempner showed are transcendental. - Kevin Ryde, Sep 16 2019

Examples

			0.234415508674864614413415474345604597614724563906693027679427737098381...
		

Crossrefs

Cf. A006467 (continued fraction), A030300 (ternary expansion).

Programs

  • Mathematica
    RealDigits[N[Sum[(-1)^n/3^(2^n), {n, 0, Infinity}], 120]][[1]] (* Amiram Eldar, Jun 11 2023 *)
  • PARI
    { default(realprecision, 20080); x=10*suminf(n=0, (-1)^n/3^(2^n)); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b160386.txt", n, " ", d)); }

A061678 Continued fraction for Sum_{n>=0} 1/3^(3^n).

Original entry on oeis.org

0, 2, 1, 2, 3, 26, 1, 2, 2, 1, 2, 19682, 1, 1, 1, 2, 2, 1, 26, 3, 2, 1, 2, 7625597484986, 1, 1, 1, 2, 3, 26, 1, 2, 2, 1, 1, 1, 19682, 2, 1, 2, 2, 1, 26, 3, 2, 1, 2, 443426488243037769948249630619149892802, 1, 1, 1, 2, 3, 26, 1, 2, 2, 1, 2, 19682
Offset: 0

Views

Author

Jason Earls, Jun 23 2001

Keywords

Comments

The continued fraction has a "folded" overall structure. Apart from a(0) and from the record values of the form 3^(3^k)-1 (k >= 0), the only terms are 1 and 3. This follows from the theorem in Shallit's paper. - Georg Fischer, Aug 29 2022

Examples

			0.370421175633926798495743189411...
		

Crossrefs

Programs

  • Mathematica
    ContinuedFraction[Sum[1/3^(3^i), {i, 0, 5}]] (* Michael De Vlieger, Jul 01 2018 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 8000); x=contfrac(suminf(n=0, 1/3^(3^n))); for (n=0, 382, write("b061678.txt", n, " ", x[n+1])) } \\ Harry J. Smith, Jul 26 2009
Showing 1-2 of 2 results.