First power of 2 that has leading decimal digits of 12: Difference between revisions

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 The  678,910th  occurrence of 2 raised to a power whose product starts with "123" is 193,060,223
 //64Bit real    0m43,031s //32Bit real	0m13,363s</pre>
+===alternative===
+Using only the first digits of 2**i in an Uint64 suffices.
+<lang pascal>program Power2Digits;
+uses
+  sysutils,strUtils;
+function FindExp(CntLmt:NativeUint;Number : AnsiString):NativeUint;
+var
+  probe : Uint64;
+  i,cnt: NativeUInt;
+begin
+  cnt := 0;
+  i := 0;
+  Probe := 1;
+  repeat
+    inc(Probe,Probe);
+    inc(i);
+    // if 2**i gets to big divide by one digit = 10
+    If Probe >= 1000*1000*1000 *1000*1000*1000 then
+      Probe := Probe DIV 10;
+    //Check the first characters of the number
+    IF COPY(IntToStr(Probe),1,Length(number)) = Number then
+    Begin
+      inc(cnt);
+      IF cnt>= CntLmt then
+        BREAK;
+    end;
+  until false;
+  write('The ',Numb2USA(IntToStr(cnt)),'th  occurrence of 2 raised to a power');
+  write(' whose product starts with "',Numb2USA(number));
+  writeln('" is ',Numb2USA(IntToStr(i)));
+  FindExp := i;
+end;
+Begin
+  FindExp(1,'12');
+  FindExp(2,'12');
+  FindExp(45,'123');
+  FindExp(12345,'123');
+  FindExp(678910,'123');
+end.</lang>
+{{out}}
+<pre>The 1th  occurrence of 2 raised to a power whose product starts with "12" is 7
+The 2th  occurrence of 2 raised to a power whose product starts with "12" is 80
+The 45th  occurrence of 2 raised to a power whose product starts with "123" is 12,710
+The 12,345th  occurrence of 2 raised to a power whose product starts with "123" is 3,510,491
+The 678,910th  occurrence of 2 raised to a power whose product starts with "123" is 193,060,223
+real    0m22,931s
+//Without IF COPY(IntToStr(Probe),1,Length(number)) = Number then
+FindExp(193060223,'123') takes
+real	0m0,212s</pre>
 =={{header|REXX}}==