%I #54 Nov 30 2017 04:06:43
%S 1,11,29,76,199,521,1364,3571,9349,24476,64079,167761,439204,1149851,
%T 3010349,7881196,20633239,54018521,141422324,370248451,969323029,
%U 2537720636,6643838879,17393796001,45537549124,119218851371,312119004989,817138163596,2139295485799,5600748293801
%N Numbers n such that the quintic polynomial x^5 - 10*n*x^2 - 24*n has Galois group A_5 over rationals.
%C Sequence appears to agree with the Lucas bisection A002878 for n > 1. - _Klaus Brockhaus_, Nov 18 2007
%C 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
%C 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
%C 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
%C The relation with A002878 is proved in Wong's article. - _Eric M. Schmidt_, Nov 25 2017
%H Siman Wong, <a href="https://dx.doi.org/10.1090/proc/13677">Specialization of Galois groups and integral points on elliptic curves</a>, Proceedings of the American Mathematical Society, 145 (2017), 5179-5190.
%o (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
%Y Cf. A134538, A134547, A002878.
%K nonn
%O 1,2
%A _Artur Jasinski_, Nov 15 2007
%E a(20) corrected by _Klaus Brockhaus_, Nov 18 2007
%E Unjustified formulas, programs, and b-file deleted. - _N. J. A. Sloane_, Mar 04 2017