This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A145996 #9 Nov 06 2013 14:57:01
%S A145996 0,1,2,4,243
%N A145996 Numbers k such that quintic polynomial 4*k - k^2 + 5*k^2*x + (20*k - 20*k^2)*x^3 + (16 - 32*k + 16*k^2)*x^5 has a rational root.
%C A145996 When k = 1 the polynomial degenerates to degree 1.
%C A145996 Conjecture: This sequence is finite and complete.
%C A145996 This sequence is not the same as A005275 because 198815685282 does not belong to this sequence.
%C A145996 No more values of k less than 2*10^7.
%C A145996 One of the root of quintic polynomial 4 k - k^2 + 5 k^2 x + (20 k - 20 k^2) x^3 + (16 - 32 k + 16 k^2) x^5 is Hypergeometric2F1(1/5,4/5,1/2,1/k).
%C A145996 Precisely for k belonging to this sequence, Hypergeometric2F1(1/5,4/5,1/2,1/k) is algebraic number of 4 degree, otherwise it is of degree 5. [_Artur Jasinski_, Oct 26 2008]
%C A145996 = sqrt(k/(k-1)) cos(3/5 arcsin(1/sqrt(k))). [_Artur Jasinski_, Oct 29 2008]
%t A145996 a = {}; Do[If[Length[FactorList[(4 k - k^2 + 5 k^2 x + (20 k - 20 k^2) x^3 + (16 - 32 k + 16 k^2) x^5)]] > 2, AppendTo[a, k]; Print[k]], {k, 1, 20000000}]; a
%Y A145996 Cf. A146160.
%K A145996 nonn
%O A145996 1,3
%A A145996 _Artur Jasinski_, Oct 26 2008