36 lines
1.3 KiB
Text
36 lines
1.3 KiB
Text
using Formatting
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import Base.iterate, Base.IteratorSize, Base.IteratorEltype, Base.Iterators.take
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const metallicnames = ["Platinum", "Golden", "Silver", "Bronze", "Copper", "Nickel",
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"Aluminium", "Iron", "Tin", "Lead"]
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struct Lucas b::Int end
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Base.IteratorSize(s::Lucas) = Base.IsInfinite()
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Base.IteratorEltype(s::Lucas) = BigInt
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Base.iterate(s::Lucas, (x1, x2) = (big"1", big"1")) = (t = x2 * s.b + x1; (x1, (x2, t)))
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printlucas(b, len=15) = (for i in take(Lucas(b), len) print(i, ", ") end; println("..."))
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function lucasratios(b, len)
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iter = BigFloat.(collect(take(Lucas(b), len + 1)))
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return map(i -> iter[i + 1] / iter[i], 1:length(iter)-1)
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end
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function metallic(b, dplaces=32)
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setprecision(dplaces * 5)
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ratios, err = lucasratios(b, dplaces * 50), BigFloat(10)^(-dplaces)
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errors = map(i -> abs(ratios[i + 1] - ratios[i]), 1:length(ratios)-1)
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iternum = findfirst(x -> x < err, errors)
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println("After $(iternum + 1) iterations, the value of ",
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format(ratios[iternum + 1], precision=dplaces),
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" is stable to $dplaces decimal places.\n")
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end
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for (b, name) in enumerate(metallicnames)
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println("The first 15 elements of the Lucas sequence named ",
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metallicnames[b], " and b of $(b - 1) are:")
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printlucas(b - 1)
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metallic(b - 1)
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end
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println("Golden ratio to 256 decimal places:")
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metallic(1, 256)
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