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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 (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-Fran├žois 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

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 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

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=(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: A093684 A101270 A155522 * A204689 A109718 A053385

Adjacent sequences:  A007521 A007522 A007523 * A007525 A007526 A007527

KEYWORD

nonn,cons,changed

AUTHOR

N. J. A. Sloane.

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 April 17 20:01 EDT 2014. Contains 240655 sequences.