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A135064 Numbers n such that the quintic polynomial x^5 - 10*n*x^2 - 24*n has Galois group A_5 over rationals. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence appears to agree with the Lucas bisection A002878 for n > 1. - Klaus Brockhaus, Nov 18 2007

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

The relation with A002878 is proved in Wong's article. - Eric M. Schmidt, Nov 25 2017

LINKS

Table of n, a(n) for n=1..30.

Siman Wong, Specialization of Galois groups and integral points on elliptic curves, Proceedings of the American Mathematical Society, 145 (2017), 5179-5190.

PROG

(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

CROSSREFS

Cf. A134538, A134547, A002878.

Sequence in context: A239734 A106880 A275475 * A179502 A053703 A216559

Adjacent sequences:  A135061 A135062 A135063 * A135065 A135066 A135067

KEYWORD

nonn

AUTHOR

Artur Jasinski, Nov 15 2007

EXTENSIONS

a(20) corrected by Klaus Brockhaus, Nov 18 2007

Unjustified formulas, programs, and b-file deleted. - N. J. A. Sloane, Mar 04 2017

STATUS

approved

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Last modified May 26 10:10 EDT 2019. Contains 323579 sequences. (Running on oeis4.)