

A007524


Decimal expansion of log_10 2.
(Formerly M2196)


26



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
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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. [JeanFrançois 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. 7276 (or No. 116 1999 pp. 7275), Paris.
M. E. Lines, A Number For Your Thought, pp. 4352 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. 5761, BelinPour La Science, Paris 2000.


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 & T. Walsh, Benford's Law
T. P. Hill, The first digital phenomenon
T. P. Hill, The FirstDigit Phenomenon
T. P. Hill, The FirstDigit Phenomenon(Accompanying Diagrams)
R. Matthews, The Power of One
S. J. Miller, Some Thoughts on benford's Law
M. J. Nigrini, Benford's Law
I. Peterson, Mathtrek, First Digits
L. Pietronero et al., The Uneven Distribution of Numbers in Nature
Simon Plouffe, The log10 of 2 to 2000 digits
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=(xd)*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: A093684 A101270 A155522 * A204689 A109718 A053385
Adjacent sequences: A007521 A007522 A007523 * A007525 A007526 A007527


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Definition corrected by Franklin T. AdamsWatters, Apr 13 2006
Final digits of sequence corrected using the bfile.  N. J. A. Sloane, Aug 30 2009


STATUS

approved



