OFFSET
0,1
COMMENTS
Log_10 (2) is the probability that 1 be first significant digit occurring in data collections (Benford's law). - Lekraj Beedassy, Jan 21 2005
When adding two sound power sources of x decibels, the resulting sound power is x + 10*log_10(2), that is x + 3.01... decibels. - Jean-François Alcover, Jun 21 2013
In engineering (all branches, but particularly electronic and electrical) power and amplitude ratios are measured rigorously in decibels (dB). This constant, with offset 1 (i.e., 3.01... = 10*A007524) is the dB equivalent of a 2:1 power ratio or, equivalently, sqrt(2):1 amplitude ratio. - Stanislav Sykora, Dec 11 2013
REFERENCES
T. Hill, "Manipulation, or the First Significant Numeral Determines the Law", in 'La Recherche', No. 2 1999 pp. 72-76 (or No. 116 1999 pp. 72-75), Paris.
M. E. Lines, A Number For Your Thought, pp. 43-52 Institute of Physics Pub. London 1990.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
I. Stewart, L'univers des nombres, "1 est plus probable que 9", pp. 57-61, Belin-Pour La Science, Paris 2000.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, p. 27.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..20000
K. Brown, Benford's Law.
C. K. Caldwell, The Prime Glossary, Benford's law.
I. Gent and T. Walsh, Benford's Law. [Broken link]
T. P. Hill, The first digital phenomenon. [Broken link]
T. P. Hill, The First-Digit Phenomenon.
T. P. Hill, The First-Digit Phenomenon (Accompanying Diagrams).
R. Matthews, The Power of One.
S. J. Miller, Some Thoughts on benford's Law. [Broken link]
M. J. Nigrini, Benford's Law. [Broken link]
I. Peterson, Mathtrek, First Digits. [Broken link]
L. Pietronero et al., The Uneven Distribution of Numbers in Nature, arXiv:cond-mat/9808305 [cond-mat.stat-mech], 1998.
Simon Plouffe, The LOG of 2(in base 10).
J. Walthoe, Looking out for number one.
Eric Weisstein's World of Mathematics, Benford's Law.
Eric Weisstein's World of Mathematics, Mersenne Number.
Wikipedia, Benford's law.
Wikipedia, Decibel.
FORMULA
log_10(2) = log(2)/log(10) = log(2)/(log(2) + log(5)).
EXAMPLE
0.3010299956639811952137388947244930267681898814621085413104274611271...
MATHEMATICA
RealDigits[Log[10, 2], 10, 120][[1]] (* Harvey P. Dale, Dec 19 2011 *)
PROG
(PARI) default(realprecision, 20080); x=log(2)/log(10); d=0; for (n=0, 20000, x=(x-d)*10; d=floor(x); write("b007524.txt", n, " ", d)); \\ Harry J. Smith, Apr 15 2009
CROSSREFS
Cf. decimal expansion of log_10(m): this sequence, A114490 (m = 3), A114493 (m = 4), A153268 (m = 5), A153496 (m = 6), A153620 (m = 7), A153790 (m = 8), A104139 (m = 9), A154182 (m = 11), A154203 (m = 12), A154368 (m = 13), A154478 (m = 14), A154580 (m = 15), A154794 (m = 16), A154860 (m = 17), A154953 (m = 18), A155062 (m = 19), A155522 (m = 20), A155677 (m = 21), A155746 (m = 22), A155830 (m = 23), A155979 (m = 24).
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
Definition corrected by Franklin T. Adams-Watters, Apr 13 2006
Final digits of sequence corrected using the b-file. - N. J. A. Sloane, Aug 30 2009
STATUS
approved