Initial data commit

Task/Metallic-ratios/Mathematica/metallic-ratios.math

@@ -0,0 +1,32 @@
+ClearAll[FindMetallicRatio]
+FindMetallicRatio[b_, digits_] :=
+ Module[{n, m, data, acc, old, done = False},
+  {n, m} = {1, 1};
+  old = -100;
+  data = {};
+  While[done == False,
+   {n, m} = {m, b m + n};
+   AppendTo[data, {m, m/n}];
+   If[Length[data] > 15,
+    If[-N[Log10[Abs[data[[-1, 2]] - data[[-2, 2]]]]] > digits,
+     done = True
+     ]
+    ]
+   ];
+  acc = -N[Log10[Abs[data[[-1, 2]] - data[[-2, 2]]]]];
+  <|"sequence" -> Join[{1, 1}, data[[All, 1]]],
+   "ratio" -> data[[All, 2]], "acc" -> acc,
+   "steps" -> Length[data]|>
+  ]
+Do[
+ out = FindMetallicRatio[b, 32];
+ Print["b=", b];
+ Print["b=", b, " first 15=", Take[out["sequence"], 15]];
+ Print["b=", b, " ratio=", N[Last[out["ratio"]], {\[Infinity], 33}]];
+ Print["b=", b, " Number of steps=", out["steps"]];
+ ,
+ {b, 0, 9}
+ ]
+out = FindMetallicRatio[1, 256];
+out["steps"]
+N[out["ratio"][[-1]], 256]