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.

A152566 Decimal expansion of log_3(10).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 28 2009

Keywords

Examples

			2.0959032742893846042965675220214012506075180067979301169235...

Links

Crossrefs

Cf. A102524, A100831, A113209, A102525, A152565, A113210, A152566, A152549, A152564.

Programs

A102447 Decimal expansion of log_3(20).

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Feb 23 2005

Keywords

Comments

Hausdorff dimension of Menger sponge.

Examples

			2.72683302786084204139609463636416210490710364692981054479420028247...

References

  • Manfred Schroeder, Fractals, Chaos, Power Laws, Freeman,1991, p. 179.
  • Ian Stewart, Does God Play Dice?, The New Mathematics of Chaos, 2nd Ed., Blackwell Pub'l., Malden MA, 2002, p. 207.

Links

Crossrefs

Cf. A100831, A102525, A113210, A152564.

Programs

  • Mathematica
    RealDigits[ Log[3, 20], 10, 111][[1]]
  • PARI
    log(20)/log(3) \\ Michel Marcus, Jul 19 2020

A228375 Decimal expansion of log_3(25).

Original entry on oeis.org

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

Views

Author

Vincenzo Librandi, Aug 29 2013

Keywords

Examples

			2.92994704143585433439408081535728079261586473333209937810578078959098...

Links

Crossrefs

Cf. decimal expansion of log_3(m): A102525 (m=2), A100831 (m=4), A113209 (m=5), A153459 (m=6), A152565 (m=7), A113210 (m=8), A152566 (m=10), A154175 (m=11), A154196 (m=12), A154217 (m=13), A154463 (m=14), A154542 (m=15), A154751 (m=16), A154848 (m=17), A152549 (m=18), A155003 (m=19), A102447 (m=20), A155541 (m=21), A155694 (m=22), A155808 (m=23), A155922 (m=24), this sequence, A152564 (m=26).

Programs

  • Mathematica
    RealDigits[Log[3, 25], 10, 100][[1]]

Formula

Equals 2*A113209. - R. J. Mathar, Sep 08 2013

A381517 Perimeter of the Sierpiński carpet at iteration n.

Original entry on oeis.org

4, 16, 80, 496, 3536, 26992, 212048, 1684720, 13442768, 107437168, 859182416, 6872514544, 54977282000, 439809752944, 3518452514384, 28147543587568, 225180119118032, 1801440264196720, 14411520047331152, 115292154179921392, 922337214843187664, 7378697662956950896, 59029581136289955920, 472236648588222693616
Offset: 0

Views

Author

Jakub Buczak, Feb 26 2025

Keywords

Comments

Carpet n has an overall size 3^n X 3^n and the perimeter here includes the perimeter of all holes within it.
Carpet n=0 is a unit square and has perimeter a(0) = 4.
Carpet n can be constructed by arranging 8 copies of carpet n-1 in a square with a hole in the middle,
X X X
X X
X X X
There are no gaps in each side so 2 sides of each n-1 are now not on the perimeter so a(n) = 8*a(n-1) - 16*3^(n-1).
An equivalent construction is to replace each of the 8^(n-1) unit squares of carpet n-1 with a 3 X 3 block of unit squares with a hole in the middle, so that a(n) = 3*a(n-1) + 4*8^(n-1).
A fractal is obtained by scaling the whole carpet down to a unit square and its scaled perimeter a(n)/3^n -> oo shows the perimeter is infinite even though the area is bounded.

Examples

			For n=0, a(0) = 4, the geometric representation is a square.
For n=3, a(3) = 496.

Links

Crossrefs

Cf. A001018, A271939, A293143, A365606.
Cf. A113210 (fractal dimension).

Programs

  • Python
    a = lambda n: (4 * (4 * 3**n + 8**n)) // 5

Formula

a(n) = (4/5)*(4*3^n + 8^n).
a(n) = A365606(n+1) - 4.
Showing 1-4 of 4 results.

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

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