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A135064
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Numbers n such that the quintic polynomial x^5 - 10*n*x^2 - 24*n has Galois group A_5 over rationals.
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2
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1, 11, 29, 76, 199, 521, 1364, 3571, 9349, 24476, 64079, 167761, 439204, 1149851, 3010349, 7881196, 20633239, 54018521, 141422324, 370248451, 969323029, 2537720636, 6643838879, 17393796001, 45537549124, 119218851371, 312119004989, 817138163596, 2139295485799, 5600748293801
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OFFSET
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1,2
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COMMENTS
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A002878(n) is in this sequence for all 1 < n <= 1000, and the sequences agree through a(20) = 370248451. Of course this is not a proof. - Charles R Greathouse IV, Mar 03 2017, updated Mar 20 2017
If this agreement is provable then of course it provides recurrences, generating functions, etc., for this sequence. - N. J. A. Sloane, Nov 24 2007 However, at present this is only a conjecture, and should not be used as the basis for formulas or computer programs. - N. J. A. Sloane, Mar 04 2017
Comparing A135064 with A002878, the number 4 is missing. In this case the Galois group of the quintic polynomial x^5 - 40*x^2 - 96 is dihedral of order 10. - Artur Jasinski, May 27 2010
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LINKS
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PROG
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(PARI) is(n)=my(p=Pol([1, 0, 0, -10*n, 0, -24*n])); polisirreducible(p) && polgalois(p)[1]==60 \\ Charles R Greathouse IV, Mar 03 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Unjustified formulas, programs, and b-file deleted. - N. J. A. Sloane, Mar 04 2017
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STATUS
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approved
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