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%I #21 Oct 03 2019 17:49:14
%S 8,4,32,8,40,16,64,16,96,20,96,32,96,32,160,32,128,48,160,40,256
%N Algebraic degree of R(e^(-n * Pi)), where R(q) is the Rogers-Ramanujan continued fraction.
%C All numbers in this sequence are divisible by 4.
%C All polynomials are symmetric and reducible in rationals extended by 5^(1/2) and 5^(1/4).
%D Computed by Michael Trott.
%H M. Trott, <a href="https://www.mathematica-journal.com/issue/v9i2/Corner9-2.html">Modular Equations of the Rogers-Ramanujan Continued Fraction</a>, The Mathematica Journal, 9:2, 314-333, 2004.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>
%e R(e^(-Pi))=Root[1-14*#1+22*#1^2-22*#1^3+30*#1^4+22*#1^5+22*#1^6+14*#1^7+#1^8&,4], so a(1)=8.
%e R(e^(-2*Pi))=Root[1-2*#1-6*#1^2+2*#1^3+#1^4&,3], so a(2)=4.
%t (* Program not suitable to compute more than a few terms *)
%t terms = 12; prec = 3000; QP = QPochhammer;
%t R[q_] := q^(1/5)*QP[q, q^5]*QP[q^4, q^5]/(QP[q^2, q^5]*QP[q^3, q^5]);
%t a[n_] := N[R[E^(-n Pi)], prec] // RootApproximant // MinimalPolynomial[#, x]& // Exponent[#, x]&;
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, terms}] (* _Jean-François Alcover_, Dec 22 2017 *)
%Y Cf. A275713 (degree of R(e^(-prime(n) * Pi))).
%K nonn,more,nice
%O 1,1
%A _Eric W. Weisstein_, Apr 10 2003
%E a(11)-a(21) computed by _Artur Jasinski_, Aug 24 2016
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