A084540 a(n) is the algebraic order of the elliptic lambda function lambda^*(n), where lambda^*(n) is the value of k_n such that K'(k_n)/K(k_n) = sqrt(n), K(k) is a complete elliptic function and K'(k) is the complementary function.

2, 2, 4, 2, 8, 4, 4, 4, 8, 4, 12, 4, 8, 8, 8, 4, 16, 4, 12, 8, 16, 4, 12, 8, 8, 12, 12, 4, 24, 8, 12, 8, 16, 8, 24, 8, 8, 12, 16, 8, 32, 8, 12, 12, 16, 8, 20, 8, 16, 12, 24, 8, 24, 12, 16, 16, 16, 4, 36, 8, 24, 16, 16, 8, 32, 16, 12, 16, 32, 8, 28, 8, 16, 20, 24, 12, 32, 8, 20, 16, 24, 8, 36, 16, 16, 20, 24, 8, 48, 16, 24, 12, 16, 16, 32, 16, 16, 16, 24, 8

Offset

1,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Elliptic Lambda Function

Example

k_3 = 1/4 Sqrt[2](Sqrt[3]-1) = Root[1-16*#1^2+16*#1^4&,3], so a(3) = 4.

Mathematica

Table[Exponent[MinimalPolynomial[RootApproximant[N[Sqrt[ModularLambda[I*Sqrt[n]]], 100*n]], x], x], {n, 1, 50}] (* Vaclav Kotesovec, Apr 07 2018 *)

Crossrefs

Cf. A115977.

Sequence in context: A270365 A200147 A235063 * A364557 A297112 A259192

Adjacent sequences: A084537 A084538 A084539 * A084541 A084542 A084543

Keyword

nonn

Author

Eric W. Weisstein, May 29 2003

Extensions

a(29)-a(100) from Vaclav Kotesovec, Apr 07 2018

Status

approved