Data commit

Task/Mertens-function/Delphi/mertens-function.delphi

@@ -0,0 +1,95 @@
+program Mertens_function;
+
+{$APPTYPE CONSOLE}
+
+uses
+  System.SysUtils;
+
+type
+  TMertens = record
+    merts: TArray<Integer>;
+    zeros, crosses: Integer;
+    class function Mertens(_to: Integer): TMertens; static;
+  end;
+
+{ TMertens }
+
+class function TMertens.Mertens(_to: Integer): TMertens;
+var
+  sum, zeros, crosses: Integer;
+begin
+  if _to < 1 then
+    _to := 1;
+
+  sum := 0;
+  zeros := 0;
+  crosses := 0;
+
+  SetLength(Result.merts, _to + 1);
+  var primes := [2];
+  for var i := 1 to _to do
+  begin
+    var j := i;
+    var cp := 0;
+    var spf := false;
+    for var p in primes do
+    begin
+      if p > j then
+        Break;
+      if j mod p = 0 then
+      begin
+        j := j div p;
+        inc(cp);
+      end;
+
+      if j mod p = 0 then
+      begin
+        spf := true;
+        Break;
+      end;
+    end;
+    if (cp = 0) and (i > 2) then
+    begin
+      cp := 1;
+      SetLength(primes, Length(primes) + 1);
+      primes[High(primes)] := i;
+    end;
+
+    if not spf then
+    begin
+      if cp mod 2 = 0 then
+        inc(sum)
+      else
+        dec(sum);
+    end;
+
+    Result.merts[i] := sum;
+    if sum = 0 then
+    begin
+      inc(zeros);
+      if (i > 1) and (Result.merts[i - 1] <> 0) then
+        inc(crosses);
+    end;
+  end;
+  Result.zeros := zeros;
+  Result.crosses := crosses;
+end;
+
+begin
+  var m := TMertens.mertens(1000);
+  writeln('Mertens sequence - First 199 terms:');
+  for var i := 0 to 199 do
+  begin
+    if i = 0 then
+    begin
+      write('    ');
+      Continue;
+    end;
+    if i mod 20 = 0 then
+      writeln;
+    write(format(' %3d', [m.merts[i]]));
+  end;
+  writeln(#10#10'Equals zero ', m.zeros, ' times between 1 and 1000');
+  writeln(#10'Crosses zero ', m.crosses, ' times between 1 and 1000');
+  {$IFNDEF UNIX} readln; {$ENDIF}
+end.