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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).

For algebraic degree of R[e^(-p Pi)] where p are successive n-th primes see A275713

REFERENCES

Computed by Michael Trott.

LINKS

Table of n, a(n) for n=1..21.

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-Fran├žois Alcover, Dec 22 2017 *)

CROSSREFS

Cf. A275713.

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 March 26 00:20 EDT 2019. Contains 321478 sequences. (Running on oeis4.)