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A134294 "Maximal" Hamilton numbers. Differs from usual Hamilton numbers starting at n=4. 1
2, 3, 5, 10, 44, 906, 409181, 83762797734 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified October 23 20:09 EDT 2019. Contains 328373 sequences. (Running on oeis4.)