Frobenius number for three numbers

Simple algoritm based on continued fractions was proposed by Rödseth, O. J. On a linear Diophantine problem of Frobenius J. Reine Angew. Math., 1978, 301, 171-178

All algorithm are described in Ramrez Alfonsn, J. L. The Diophantine Frobenius problem Oxford University Press, 2005

I think that Mathematica uses Rödseth's algoritm http://demonstrations.wolfram.com/PositiveFrobeniusNumbersOfThreeArguments/

This is addressed in our paper

Frobenius numbers by lattice point enumeration, David Einstein, Daniel Lichtblau, Adam Strzebonski, and Stan Wagon, INTEGERS, 7 (2007) #A15, 63 pp. <http://www.integers-ejcnt.org/vol7.html>

Rödseth formula for Frobenius numbers is good not only for computation. It allows to find weak asymptotic for Frobenius numbers with three arguments and density function for normalized Frobenius numbers.

A. V. Ustinov, “The solution of Arnold's problem on the weak asymptotics of Frobenius numbers with three arguments”, Mat. Sb., 200:4 (2009), 131–160

Shchur, V.; Sinai, Y.; Ustinov, A. Limiting distribution of Frobenius numbers for n = 3 Journal of Number Theory, 2009, 129, 2778–2789