A154751 Decimal expansion of log_3(16).

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

Offset: 1

Author

N. J. A. Sloane, Oct 30 2009

Keywords

• nonn
• cons

Comments

From Jianing Song, Oct 12 2019: (Start)

log_3(16) is the Hausdorff dimension of the 4D Cantor dust. In general, the n-dimensional Cantor dust has Hausdorff dimension n*log_3(2).

Also, 1 + log_3(16) = log_3(48) is the Hausdorff dimension of the 4D analog of the Menger sponge. In general, let S_n = {(Sum_{j>=1} d_(1j)/3^j, Sum_{j>=1} d_(2j)/3^j, ..., Sum_{j>=1} d_(nj)/3^j) where d_(ij) is either -1, 0 or 1, Sum_{i=1..n} |d_(ij)| >= n-1 for all j}, then the image of S_n is the n-dimensional Menger sponge, whose Hausdorff dimension is log_3(2^n+n*2^(n-1)) = (n-1)*log_3(2) + log_3(n+2). n = 2 gives the Sierpiński carpet, and n = 3 gives the original Menger sponge. See pages 10-12 of the arXiv link below, which gives an alternative construction of the n-dimensional Menger sponge and an illustration of the 4-dimensional Menger sponge. (End)

Examples

			2.5237190142858297483981084573710434171983425605275217114826...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Yun Yang, Yanhua Yu, The generalization of Sierpinski carpet and Sierpinski triangle in n-dimensional space, arXiv:1702.04901 [math.DG], 2017.
• Index entries for transcendental numbers

Programs

Mathematica

RealDigits[Log[3, 16], 10, 120][[1]] (* Vincenzo Librandi, Aug 29 2013 *)