Viswanath’s constant

Viswanath’s constant V1.1319882487943 is a real number whose nth power approximates the absolute valueMathworldPlanetmathPlanetmathPlanetmath of the nth term of some random Fibonacci sequencesMathworldPlanetmath, especially as n gets larger. In his 2000 paper, Divakar Viswanath gave the value of the functionMathworldPlanetmath to just eight decimal places as 1.13198824. Viswanath believed the logarithm of the constant to lie between 0.123975598 and 0.1239755995. Oliveira and Figuereido in 2002 computed the value again using interval arithmetic instead of Viswanath’s “detailed rounding-error analysis,” in order to obtain “slightly better results.” Using Mathematica, Eric Weisstein computed a different value: 1.1321506910656020459.

The continued fractionDlmfMathworldPlanetmath of Viswanath’s constant, which is not periodic, begins


and aside from some instances of 2s, is thought to contain mostly odd numbersMathworldPlanetmathPlanetmath.


  • 1 S. R. Finch, Mathematical Constants. Cambridge: Cambridge University Press (2003): 1.2.4
  • 2 João Batista Oliveira & Luiz Henrique de Figuereido, “Interval Computation of Viswanath’s Constant” Reliable Computing 8 2 (2002): 131 - 138
  • 3 Divakar Viswanath “Random Fibonacci sequences and the number 1.13198824….” Mathematics of Computation 69 231 (2000): 1131 - 1155
Title Viswanath’s constant
Canonical name ViswanathsConstant
Date of creation 2013-03-22 18:09:32
Last modified on 2013-03-22 18:09:32
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11B39
Synonym Viswanath constantMathworldPlanetmath