A134294 - OEIS

%I #11 May 07 2018 04:45:37

%S 2,3,5,10,44,906,409181,83762797734

%N "Maximal" Hamilton numbers. Differs from usual Hamilton numbers starting at n=4.

%C a(n) is the minimal degree of an equation from which n successive terms after the first can be removed (by a series of transformation comparable to Tschirnhaus's) without requiring the solution of at least one irreducible equation of degree greater than n. The cases where an equation of degree greater than n is needed but is in fact factorizable into several equations of degree all less than or equal to n are considered as fair. a(n) <= A000905(n) by definition.

%D W. R. Hamilton, Sixth Report of the British Association for the Advancement of Science, London, 1831, 295-348.

%H Raymond Garver, <a href="http://www.jstor.org/stable/1968002">The Tschirnhaus transformation</a>, The Annals of Mathematics, 2nd Ser., Vol. 29, No. 1/4. (1927 - 1928), pp. 330.

%H E. Lucas, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k29021h">Théorie des Nombres</a>, Gauthier-Villars, Paris, 1891, Vol. 1, p. 496.

%H J. J. Sylvester and M. J. Hammond, <a href="http://www.jstor.org/stable/90558">On Hamilton's numbers</a>, Phil. Trans. Roy. Soc., 178 (1887), 285-312.

%e a(4)=10 because one can remove 4 terms in an equation of degree 10 by solving two quartic equations.

%Y Cf. A000905.

%K more,nice,nonn

%O 1,1

%A _Olivier Gérard_, Oct 17 2007