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%I A007524 M2196 #68 Aug 24 2023 11:54:14
%S A007524 3,0,1,0,2,9,9,9,5,6,6,3,9,8,1,1,9,5,2,1,3,7,3,8,8,9,4,7,2,4,4,9,3,0,
%T A007524 2,6,7,6,8,1,8,9,8,8,1,4,6,2,1,0,8,5,4,1,3,1,0,4,2,7,4,6,1,1,2,7,1,0,
%U A007524 8,1,8,9,2,7,4,4,2,4,5,0,9,4,8,6,9,2,7,2,5,2,1,1,8,1,8,6,1,7,2,0,4,0,6,8,4
%N A007524 Decimal expansion of log_10 2.
%C A007524 Log_10 (2) is the probability that 1 be first significant digit occurring in data collections (Benford's law). - _Lekraj Beedassy_, Jan 21 2005
%C A007524 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
%C A007524 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
%D A007524 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.
%D A007524 M. E. Lines, A Number For Your Thought, pp. 43-52 Institute of Physics Pub. London 1990.
%D A007524 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007524 I. Stewart, L'univers des nombres, "1 est plus probable que 9", pp. 57-61, Belin-Pour La Science, Paris 2000.
%H A007524 Harry J. Smith, <a href="/A007524/b007524.txt">Table of n, a(n) for n = 0..20000</a>
%H A007524 K. Brown, <a href="http://www.mathpages.com/home/kmath302/kmath302.htm">Benford's Law</a>
%H A007524 C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php/BenfordsLaw.html">Benford's law</a>
%H A007524 I. Gent & T. Walsh, <a href="http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf">Benford's Law</a>
%H A007524 T. P. Hill, <a href="http://www.mccombs.utexas.edu/faculty/jonathan.koehler/docs/sta309h/Benford_1998.pdf">The first digital phenomenon</a>
%H A007524 T. P. Hill, <a href="https://web.archive.org/web/20080830025404/http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf">The First-Digit Phenomenon</a>
%H A007524 T. P. Hill, <a href="https://web.archive.org/web/20070417184651/http://www.math.gatech.edu/~hill/publications/cv.dir/1st-fig.pdf">The First-Digit Phenomenon (Accompanying Diagrams)</a>
%H A007524 R. Matthews, <a href="http://www.fortunecity.com/emachines/e11/86/one.html">The Power of One</a>
%H A007524 S. J. Miller, <a href="http://www.math.brown.edu/~sjmiller/math/handouts/BenfordTreatiseShort.pdf">Some Thoughts on benford's Law</a>
%H A007524 M. J. Nigrini, <a href="http://www.nigrini.com/Benford&#39;s_law.htm">Benford's Law</a>
%H A007524 I. Peterson, Mathtrek, <a href="http://www.maa.org/mathland/mathtrek_6_29_98.html">First Digits</a>
%H A007524 L. Pietronero et al., <a href="https://arxiv.org/abs/cond-mat/9808305">The Uneven Distribution of Numbers in Nature</a>, arXiv:cond-mat/9808305 [cond-mat.stat-mech], 1998.
%H A007524 Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap57.html">The log10 of 2 to 2000 digits</a>
%H A007524 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/log102.txt">The LOG of 2(in base 10)</a>
%H A007524 J. Walthoe, <a href="http://plus.maths.org/issue9/features/benford">Looking out for number one</a>
%H A007524 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BenfordsLaw.html">Benford's Law</a>
%H A007524 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a>
%H A007524 Wikipedia, <a href="http://en.wikipedia.org/wiki/Benford&#39;s_law">Benford's law</a>
%H A007524 Wikipedia, <a href="http://en.wikipedia.org/wiki/Decibel">Decibel</a>
%H A007524 <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>
%H A007524 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A007524 log_10(2) = log(2)/log(10) = log(2)/(log(2) + log(5)).
%e A007524 0.3010299956639811952137388947244930267681898814621085413104274611271...
%t A007524 RealDigits[Log[10, 2], 10, 120][[1]] (* _Harvey P. Dale_, Dec 19 2011 *)
%o A007524 (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
%Y A007524 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).
%K A007524 nonn,cons
%O A007524 0,1
%A A007524 _N. J. A. Sloane_
%E A007524 Definition corrected by _Franklin T. Adams-Watters_, Apr 13 2006
%E A007524 Final digits of sequence corrected using the b-file. - _N. J. A. Sloane_, Aug 30 2009

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