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A082682
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Algebraic degree of R(e^(-n * Pi)), where R(q) is the Rogers-Ramanujan continued fraction.
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1
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8, 4, 32, 8, 40, 16, 64, 16, 96, 20, 96, 32, 96, 32, 160, 32, 128, 48, 160, 40, 256
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OFFSET
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1,1
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COMMENTS
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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).
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REFERENCES
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Computed by Michael Trott.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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(* 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]&;
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CROSSREFS
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Cf. A275713 (degree of R(e^(-prime(n) * Pi))).
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KEYWORD
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nonn,more,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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