cp's OEIS Frontend

A020857 Decimal expansion of log_2(3).

%I A020857 #89 Mar 22 2025 13:05:08
%S A020857 1,5,8,4,9,6,2,5,0,0,7,2,1,1,5,6,1,8,1,4,5,3,7,3,8,9,4,3,9,4,7,8,1,6,
%T A020857 5,0,8,7,5,9,8,1,4,4,0,7,6,9,2,4,8,1,0,6,0,4,5,5,7,5,2,6,5,4,5,4,1,0,
%U A020857 9,8,2,2,7,7,9,4,3,5,8,5,6,2,5,2,2,2,8,0,4,7,4,9,1,8,0,8,8,2,4
%N A020857 Decimal expansion of log_2(3).
%C A020857 The fractional part of the binary logarithm of 3 * 2^n (A007283) is the same as that of any number of the form log_2 (A007283(n)) (e.g., log_2(192) = 7.5849625...). Furthermore, a necessary but not sufficient condition for a number to be Fibbinary (A003714) is that the fractional part of its binary logarithm does not exceed that of this number. - _Alonso del Arte_, Jun 22 2012
%C A020857 Log_2(3)-1 = 0.58496... is the exponent in n^(log_2(3)-1), the asymptotic growth rate of the number of odd coefficients in (1+x)^n mod 2 (Cf. Steven Finch ref.). - _Jean-François Alcover_, Aug 13 2014
%C A020857 Equals the Hausdorff dimension of the Sierpiński triangle. - _Stanislav Sykora_, May 27 2015
%C A020857 The complexity of Karatsuba algorithm for the multiplication of two n-digit numbers is O(n^log_2(3)). - _Jianing Song_, Apr 28 2019
%D A020857 John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See pp. 24, 257.
%D A020857 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.16, p. 145.
%H A020857 Vincenzo Librandi, <a href="/A020857/b020857.txt">Table of n, a(n) for n = 1..1000</a>
%H A020857 E. G. Dunne, <a href="/DUNNE/TEMPERAMENT2.html">Pianos and Continued Fractions</a>
%H A020857 Shalom Eliahou, <a href="http://images-archive.math.cnrs.fr/Le-probleme-3n-1-y-a-t-il-des.html">Le problème 3n+1 : y a-t-il des cycles non triviaux? (III)</a>, Images des Mathématiques, CNRS, 2011 (in French).
%H A020857 Steven Finch, Pascal Sebah and Zai-Qiao Bai, <a href="http://arXiv.org/abs/0802.2654">Odd Entries in Pascal's Trinomial Triangle</a>, arXiv:0802.2654 [math.NT], 2008, p. 1.
%H A020857 Karatsuba, <a href="https://www.researchgate.net/publication/258001835_The_complexity_of_computations">The Complexity of Computations</a>, Proceedings of the Steklov Institute of Mathematics, 1995: 169-183.
%H A020857 Youngik Lee, <a href="https://doi.org/10.20944/preprints202404.1570.v1">Numerical Approach on Collatz Conjecture</a>, Preprints.org, Brown Univ., 2024. See p. 13.
%H A020857 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/log3log2.txt">log(3)/log(2) to 10000 digits</a>
%H A020857 A. M. Reiter, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/31-2/reiter.pdf">Determining the dimension of fractals generated by Pascal's triangle</a>, Fibonacci Quart, 31(2):112-120, 1993.
%H A020857 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Stolarsky-HarborthConstant.html">Stolarsky-Harborth Constant</a>
%H A020857 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PascalsTriangle.html">Pascal's Triangle</a>
%H A020857 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiSieve.html">Sierpiński Sieve</a>
%H A020857 Wikipedia, <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm">Karatsuba algorithm</a>
%H A020857 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpinski_triangle">Sierpinski triangle</a>
%H A020857 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A020857 Equals 1 / A102525. - _Bernard Schott_, Feb 02 2023
%e A020857 log_2(3) = 1.5849625007211561814537389439...
%p A020857 evalf(log[2](3), 100); # _Bernard Schott_, Feb 02 2023
%t A020857 RealDigits[Log[2, 3], 10, 100][[1]] (* _Alonso del Arte_, Jun 22 2012 *)
%o A020857 (PARI) log(3)/log(2) \\ _Michel Marcus_, Jan 11 2016
%Y A020857 Cf. decimal expansion of log_2(m): this sequence, A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).
%Y A020857 Cf. A102525.
%K A020857 nonn,cons
%O A020857 1,2
%A A020857 _N. J. A. Sloane_
%E A020857 Comment generalized by _J. Lowell_, Apr 26 2014