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A007524 Decimal expansion of log_10 2.
(Formerly M2196)
30
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
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.
LINKS
K. Brown, Benford's Law
C. K. Caldwell, The Prime Glossary, Benford's law
I. Gent & T. Walsh, Benford's Law
R. Matthews, The Power of One
M. J. Nigrini, Benford's Law
I. Peterson, Mathtrek, First Digits
L. Pietronero et al., The Uneven Distribution of Numbers in Nature, arXiv:cond-mat/9808305 [cond-mat.stat-mech], 1998.
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).
Sequence in context: A101270 A351097 A155522 * A357868 A357881 A204689
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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)