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# 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 number (being the sum of 5 and 8), and like all other odd-indexed Fibonacci numbers, it is also a Markov number. It appears in the following solutions to $13^{2}+y^{2}+z^{2}=39yz$: (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 function, but this is neither unlucky nor special (A051401 in Sloane’s OEIS lists other lows of the Mertens function).

## Mathematics Subject Classification

11A99*no label found*

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