Data commit

Task/Iterated-digits-squaring/Mathematica/iterated-digits-squaring.math

@@ -0,0 +1,37 @@
+sumDigitsSquared[n_Integer] := Total[IntegerDigits[n]^2]
+stopValues = Join[{1}, NestList[sumDigitsSquared, 89, 7]];
+iterate[n_Integer] :=
+ NestWhile[sumDigitsSquared, n, Intersection[stopValues, {#}] == {} &]
+
+numberOfDigits = 8;
+maxSum = numberOfDigits 9^2;
+loopVariables =
+  ToExpression@Table["i" <> ToString[n], {n, numberOfDigits}];
+iteratesToOne = Cases[Range@maxSum, _?(iterate[#] == 1 &)];
+allIterators =
+  Flatten[{Reverse@#, 9}] & /@ Partition[loopVariables, 2, 1];
+maxCombinations = numberOfDigits!;
+
+ssd =
+  SparseArray[Table[n^2 -> numberOfDigits, {n, 9}], {maxSum}];
+
+Do[
+  variables = loopVariables[[;; digitCount]];
+  iterators = allIterators[[;; digitCount - 1]];
+
+  Do[ssd +=
+    SparseArray[
+     Total[variables^2] ->
+      maxCombinations/
+       Times @@ (Tally[PadRight[variables, numberOfDigits]][[All,
+            2]]!), {maxSum}], {i, 9}, Evaluate[Sequence @@ iterators]],
+
+  {digitCount, 2, numberOfDigits}];
+
+onesCount =
+ Total[Cases[
+    ArrayRules[ssd] /.
+     HoldPattern[{a_} -> b_] :> {a,
+       b}, {_?(MemberQ[iteratesToOne, #] &), _}][[All, 2]]];
+
+(10^numberOfDigits - 1) - onesCount