1,1

a(n) = 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 or equal to n are considered as fair. a(n) <= A000905(n) by definition.

Raymond Garver, The Tschinrhaus transformation, The Annals of Mathematics, 2nd Ser., Vol. 29, No. 1/4. (1927 - 1928), pp. 330.

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

J. J. Sylvester and M. J. Hammond, On Hamilton's numbers, Phil. Trans. Roy. Soc., 178 (1887), 285-312.

E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 496.

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

Cf. A000905.

Sequence in context: A132183 A003504 A003182 this_sequence A130165 A083397 A067362

Adjacent sequences: A134291 A134292 A134293 this_sequence A134295 A134296 A134297

more,nice,nonn

Olivier GERARD (olivier.gerard(AT)gmail.com), Oct 17 2007