The First Digit 1

“The imagination in a mathematician who creates makes no less difference than in a poet who invents......”

....D’Alembert

Abstract

Benford’s Law or The First Digit Law as it is commonly known has been a fascination to many generations. This counter-intuitive law proposes that given a sequence of numbers (usually from a data set like length of rivers, height of mountains, populations of nations or any source of data from real life), the first digit is ‘1’ roughtly 30% of the time. Many mathematical sequences, such as Fibonacci sequences also follow Benford’s Law. Benford’s Law has some interesting applications, especially in fraud detection!

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Suggested Reading

  1. [1]

    Aditi Kar, Weyl’s Equidistribution Theorem, Resonance, Vol.8, No.5, pp.30–37, 2003.

    Article  Google Scholar 

  2. [2]

    S Kunoff, N! has the First Digit Property, The Fibonacci Quarterly, Vol.25, No.4, pp.365–367, 1987.

    Google Scholar 

  3. [3]

    R A Raimi, The First Digit Problem, Scientific American, Vol.221, No.6, pp.109–120, 1969.

    Article  Google Scholar 

  4. [4]

    Sheldon Ross, A First Course in Probability, Pearson Education, Sixth Edition, 2009.

    Google Scholar 

  5. [5]

    T Tao, Benfords law, Zipfs law, and the Pareto distribution, http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-thepareto-distribution/, 2009.

    Google Scholar 

  6. [6]

    L C Washington, Benford’s Law For Fibonacci And Lucas Numbers, The Fibonacci Quarterly, Vol.19, pp.175–177, 1981.

    Google Scholar 

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Correspondence to Tanya Kaushal Srivastava.

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Tanya Kaushal Srivastava is a BS-MS student at the Department of Mathematics, IISER Mohali and is a KVPY fellow.

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Srivastava, T.K. The First Digit 1. Reson 18, 1073–1085 (2013). https://doi.org/10.1007/s12045-013-0135-y

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Keywords

  • Random numbers
  • unpredictable
  • equidistribution
  • Weyl criterion
  • absorptive property