thirteen


Thirteen is in many ways a rather ordinary number, yet some people are afraid of it (see triskaidekaphobia). For a mathematician there is nothing particularly unlucky about 13; in fact, 13 is a lucky prime (since it is not crossed off in the well-defined sieving process for lucky numbers).

13 is a Fibonacci numberDlmfMathworldPlanetmath (being the sum of 5 and 8), and like all other odd-indexed Fibonacci numbers, it is also a Markov numberMathworldPlanetmath. It appears in the following solutions to 132+y2+z2=39yz: (1, 5, 13), (1, 13, 34), (5, 13, 194), (13, 34, 1325), (13, 194, 7561), (13, 1325, 51641), (13, 7561, 294685), (13, 51641, 2012674), (13, 294685, 11485154), (13, 2012674, 78442645), (13, 11485154, 447626321), etc. Starting with 1, the number 13 represents a new low for the Mertens functionMathworldPlanetmath, but this is neither unlucky nor special (A051401 in Sloane’s OEIS lists other lows of the Mertens function).

This is not to say that there isn’t anything special about 13: for example, it is the only integer solution to x4=n2+(n+1)2 (besides the obvious x=1 and n=0).

Title thirteen
Canonical name Thirteen
Date of creation 2013-03-22 17:24:58
Last modified on 2013-03-22 17:24:58
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Feature
Classification msc 11A99