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 A082682 Algebraic degree of R(e^(-n * Pi)), where R(q) is the Rogers-Ramanujan continued fraction. 1
 8, 4, 32, 8, 40, 16, 64, 16, 96, 20, 96, 32, 96, 32, 160, 32, 128, 48, 160, 40, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All numbers in this sequence are divisible by 4. All polynomials are symmetric and reducible in rationals extended by 5^(1/2) and 5^(1/4). REFERENCES Computed by Michael Trott. LINKS M. Trott, Modular Equations of the Rogers-Ramanujan Continued Fraction, The Mathematica Journal, 9:2, 314-333, 2004. Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction EXAMPLE 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. R(e^(-2*Pi))=Root[1-2*#1-6*#1^2+2*#1^3+#1^4&,3], so a(2)=4. MATHEMATICA (* Program not suitable to compute more than a few terms *) terms = 12; prec = 3000; QP = QPochhammer; R[q_] := q^(1/5)*QP[q, q^5]*QP[q^4, q^5]/(QP[q^2, q^5]*QP[q^3, q^5]); a[n_] := N[R[E^(-n Pi)], prec] // RootApproximant // MinimalPolynomial[#, x]& // Exponent[#, x]&; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, terms}] (* Jean-François Alcover, Dec 22 2017 *) CROSSREFS Cf. A275713 (degree of R(e^(-prime(n) * Pi))). Sequence in context: A238163 A213773 A213178 * A279635 A213505 A270232 Adjacent sequences:  A082679 A082680 A082681 * A082683 A082684 A082685 KEYWORD nonn,more,nice AUTHOR Eric W. Weisstein, Apr 10 2003 EXTENSIONS a(11)-a(21) computed by Artur Jasinski, Aug 24 2016 STATUS approved

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Last modified July 16 12:40 EDT 2020. Contains 335788 sequences. (Running on oeis4.)