A134294 - OEIS

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A134294

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

2, 3, 5, 10, 44, 906, 409181, 83762797734 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	COMMENTS	`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.`
	REFERENCES	`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.`
	LINKS	`Table of n, a(n) for n=1..8.` `E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 496.`
	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 A130165` `Adjacent sequences: A134291 A134292 A134293 * A134295 A134296 A134297`
	KEYWORD	`more,nice,nonn`
	AUTHOR	`Olivier GERARD (olivier.gerard(AT)gmail.com), Oct 17 2007`
	STATUS	`approved`

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Last modified May 25 08:17 EDT 2013. Contains 225646 sequences.