

A134294


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


1




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, 295348.


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, GauthierVillars, Paris, 1891, Vol. 1, p. 496.
J. J. Sylvester and M. J. Hammond, On Hamilton's numbers, Phil. Trans. Roy. Soc., 178 (1887), 285312.


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: A003504 A213169 A003182 * A154956 A197312 A259387
Adjacent sequences: A134291 A134292 A134293 * A134295 A134296 A134297


KEYWORD

more,nice,nonn


AUTHOR

Olivier Gérard, Oct 17 2007


STATUS

approved



