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A084540
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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.
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1
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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k_3 = 1/4 Sqrt[2](Sqrt[3]-1) = Root[1-16*#1^2+16*#1^4&,3], so a(3) = 4.
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MATHEMATICA
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Table[Exponent[MinimalPolynomial[RootApproximant[N[Sqrt[ModularLambda[I*Sqrt[n]]], 100*n]], x], x], {n, 1, 50}] (* Vaclav Kotesovec, Apr 07 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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