

A020857


Decimal expansion of log_2(3).


30



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, 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, 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
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OFFSET

1,2


COMMENTS

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
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.).  JeanFrançois Alcover, Aug 13 2014


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
E. G. Dunne, Pianos and Continued Fractions
Shalom Eliahou, Le problème 3n+1 : y atil des cycles non triviaux ? [in French]
Steven Finch, Pascal Sebah and ZaiQiao Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654) p. 1.
Simon Plouffe, log(3)/log(2) to 10000 digits
Eric Weisstein's World of Mathematics, StolarskyHarborth Constant
Eric Weisstein's World of Mathematics, Pascal's Triangle
Eric Weisstein's World of Mathematics, Sierpiński Sieve


EXAMPLE

log_2(3) = 1.5849625007211561814537389439...


MATHEMATICA

RealDigits[Log[2, 3], 10, 100][[1]] (* Alonso del Arte, Jun 22 2012 *)


CROSSREFS

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).
Sequence in context: A021635 A021175 A011095 * A096413 A222591 A186691
Adjacent sequences: A020854 A020855 A020856 * A020858 A020859 A020860


KEYWORD

nonn,cons,changed


AUTHOR

N. J. A. Sloane


EXTENSIONS

Comment generalized by J. Lowell, Apr 26 2014


STATUS

approved



