A134294 "Maximal" Hamilton numbers. Differs from usual Hamilton numbers starting at n=4.

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

Offset

1,1

Comments

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.

References

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

Links

Table of n, a(n) for n=1..8.

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

E. Lucas, Théorie des Nombres, Gauthier-Villars, Paris, 1891, Vol. 1, p. 496.

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

Example

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

Crossrefs

Cf. A000905.

Sequence in context: A348260 A363257 A344347 * A154956 A197312 A259387

Adjacent sequences: A134291 A134292 A134293 * A134295 A134296 A134297

Keyword

more,nice,nonn

Author

Olivier Gérard, Oct 17 2007

Status

approved