Minimum multiple of m where digital sum equals m: Difference between revisions

</pre>

===much faster===

<!--<lang Phix>(phixonline)-->

<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">rc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> <span style="color: #000080;font-style:italic;">-- remainder cache

-- each rc[n] is sq_rmdr({1,10,100,1000...},n) as needed,

-- with rc[n][k&gt;1] calculated from rmdr(rc[n][k-1]*10,n)

-- which avoids the need for any big number handling.

-- (actually, it turns out to be faster this way anyhows)</span>

<span style="color: #008080;">function</span> <span style="color: #000000;">rmc</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">))</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">rem</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>

<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rc</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>

<span style="color: #000000;">rc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rc</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">rcn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rcn</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">l</span> <span style="color: #008080;">then</span>

<span style="color: #000000;">rc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- kill refcount</span>

<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rcn</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">l</span> <span style="color: #008080;">do</span>

<span style="color: #000000;">rcn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rcn</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rcn</span><span style="color: #0000FF;">[$]*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>

<span style="color: #000000;">rc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rcn</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>

<span style="color: #000000;">rem</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rem</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">rcn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

<span style="color: #008080;">return</span> <span style="color: #000000;">rem</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> <span style="color: #000080;font-style:italic;">-- (for the final divide only)</span>

<span style="color: #008080;">function</span> <span style="color: #000000;">mmnn</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>

<span style="color: #000080;font-style:italic;">--

-- minimum multiple of n that sums to n

--

-- Just as we can emulate normal counting using an array of digits,

-- we can count while maintaining a sum of digits, which means we

-- have to find both an incrementable and a decrementable digit,

-- moving the latter to the end(ish), or if none such prepend a 1,

-- eg: 5 -&gt; 14 -&gt; 23 -&gt; 32 -&gt; 41 -&gt; 50 -&gt; 104 -&gt; 113 -&gt; 122 -&gt; 131

-- -&gt; 140 -&gt; 203 .. 230 -&gt; 302 .. 500 -&gt; 1004 .. 10004, etc.

-- Another example, this time summing to 14 (the above was to 5!):

-- 59 -&gt; 68 .. 95 -&gt; 149 .. 194 -&gt; 239 .. 293 -&gt; 329 .. 392

-- -&gt; 419 .. 491 -&gt; 509 .. 590 -&gt; 608 .. 680 -&gt; 707 .. 770

-- -&gt; 806 .. 860 -&gt; 905 .. 950 -&gt; 1049, etc.

-- in that last case, what we actually need to do is decrement the

-- 5 (-&gt;940), and then reverse the whole thing, then prepend a 1,

-- likewise if we increment a middle digit, dec & reverse(rest).

-- In the extreme case you would want 1 -&gt; 10 -&gt; 100 -&gt; 1000, etc,

-- although since 1 passes muster we would never actually do that.

--</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- (avoid remainder(x,0|1))

-- optimising for trailing zeroes makes a huge difference</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">n0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tz</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>

<span style="color: #008080;">while</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>

<span style="color: #000000;">n0</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">10</span>

<span style="color: #000000;">tz</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>

<span style="color: #004080;">bool</span> <span style="color: #000000;">r5</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">5</span> <span style="color: #000080;font-style:italic;">-- not quite so much...</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">ceil</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- this many trailing 9s</span>

<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">l</span> <span style="color: #000080;font-style:italic;">-- ...and this first digit</span>

<span style="color: #004080;">string</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'9'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tz</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- eg n=14 -&gt; "59"</span>

<span style="color: #000000;">l</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>

<span style="color: #004080;">atom</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>

<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">rem</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rmc</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">then</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">;</span> <span style="color: #0000FF;">?{</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (r5 optimisation)</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">dd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- decrementable digit position</span>

<span style="color: #000000;">ddd</span> <span style="color: #000080;font-style:italic;">-- decrementable digit value</span>

<span style="color: #004080;">bool</span> <span style="color: #000000;">bIncAbleFound</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>

<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">l</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">dd</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>

<span style="color: #000000;">dd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>

<span style="color: #000000;">ddd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span>

<span style="color: #008080;">else</span>

<span style="color: #000000;">bIncAbleFound</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">9</span> <span style="color: #008080;">and</span> <span style="color: #000000;">dd</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">bIncAbleFound</span> <span style="color: #008080;">or</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>

<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dd</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ddd</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">bIncAbleFound</span> <span style="color: #008080;">then</span>

<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>

<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">l</span><span style="color: #0000FF;">])</span>

<span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- (i=1 and (digits[1]=9] or no decrementable) case)</span>

<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">l</span><span style="color: #0000FF;">])</span>

<span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'1'</span><span style="color: #0000FF;">)</span>

<span style="color: #000000;">l</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #008080;">exit</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">r5</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">],</span><span style="color: #008000;">"05"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>

<span style="color: #004080;">mpz</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>

<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">return</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>

<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- 0.4s</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n%3d:"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %-11s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mmnn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)})</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">101</span> <span style="color: #008080;">to</span> <span style="color: #000000;">164</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- 0.7s, but mmnn(165) takes 1mins 25s

--for n=101 to 274 do -- 1mins 50s (most from 165, gave up on 275)</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n%3d:"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %-11s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mmnn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)})</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>

<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 1.1s</span>

<!--</lang>-->

{{out}}

<pre>

1: 1 1 1 1 1 1 1 1 1 19

11: 19 4 19 19 13 28 28 11 46 199

21: 19 109 73 37 199 73 37 271 172 1333

31: 289 559 1303 847 1657 833 1027 1576 1282 17497

41: 4339 2119 2323 10909 11111 12826 14617 14581 16102 199999

51: 17449 38269 56413 37037 1108909 142498 103507 154981 150661 1333333

61: 163918 322579 315873 937342 1076923 1030303 880597 1469116 1157971 12842857

71: 4084507 5555554 6849163 37027027 13333333 11710513 11686987 11525641 12656962 374999986

81: 12345679 60852439 72168553 82142857 117647047 93022093 103445977 227272726 112247191 1111111111

91: 658010989 652173913 731172043 849893617 2947368421 2083333228 1030927834 3969377551 11101010101 199999999999

101: 28900990099 5881372549 6796115533 18173076922 27619047619

106: 18679245283 18691495327 36111111111 44862385321 1090909090909

111: 79009009009 80356249999 78761061946 87710526307 426086956513

116: 258620688793 255547008547 414406779661 411756302521 4999999999999

121: 2809909090909 811475409754 730081300813 2419193548387 5599999999999

126: 2380873015873 3148818897637 5468749999921 5348836434031 46076923076923

131: 6106793893129 28030303030303 6766917293233 22388058880597 37037037037037

136: 44044117647058 56919700729927 36231884057971 49568345323741 571427857142857

141: 63822694964539 140140838028169 391606993006993 277777777777777 482751724137931

146: 471917801369863 401360544217687 1081081081081081 536912751677851 13333333333333333

151: 1258278145629139 3217105263157894 1307189477124183 3830512987012987 5161290322516129

156: 4423076923076923 3821656050955414 6202531582278481 5660371069181761 124999999999999993

161: 12415527950310559 12345679012345679 18404907975398773 48773170731707317

"1.1s"

</pre>

As shown commented out, it will carry on a bit further, but I gave up on 275, and it looks to me like some quite wierd patterns are starting to appear.

<pre style="font-size: 12px">

161: 12415527950310559 12345679012345679 18404907975398773 48773170731707317 430303030303030303

166: 48186144578313253 53233532874251497 119041666666666666 59165680473372781 588235235294117647

171: 169590643216374269 290691860465116279 289017341039884393 344827586206895977 1142857142857142857

176: 511363636363636363 507903954802259887 1123594938202247191 1061452513966424581 11111111111111111111

181: 2154143646408839779 3845989010989010989 3278142075956284153 5380434239130434782 37027027027027027027

186: 9677419354838172043 5347053475935828877 20744680845744680851 20105291005291005291 157894731578947368421

191: 15706806282722513089 41666666666666666614 36269424870466321243 46391752577319535567 153845641025641025641

196: 147959183673469382653 101517766497461928934 101010101010101010101 201005025125628040201 19999999999999999999999

201: 293532338308407960199 1900990099009900990099 438374384235960591133 490195588235294117647 1902439024390243902439

206: 1407766990291213592233 966183574879227052657 2836538461538461538461 10526315784688995215311 23809047619047619047619

211: 2843601895260663507109 4716933490566037735849 4225305164318779342723 9345794387803738317757 27441855813953488372093

216: 18518518518518518518518 18433179262672811059447 27518348623848623853211 27397210045662100456621 1090909090909090909090909

221: 36199049773710407239819 259009009009009009009009 40358744394618834080713 223169642857142857142812 311111111111111111111111

226: 216371681415929203539823 220264317180615859030837 307017543859649122368421 301310043668117903930131 3043434782608695652173913

231: 1904329004329004329004329 1293103448275861637931034 429184549351931330472103 1282047008547008547008547 2978723404255319148893617

236: 2923728813135593220338983 2531223628270042194092827 3361302521008403361302521 3682004184100418410041841 41666666666666666666666662

241: 4149377593360995846473029 19421487603305785123553719 4115226337448559670781893 20491803278688483606557377 32648979591836734693877551

246: 35731300813008130081300813 32388258704048582995951417 80604838306451612903225806 35742971887550200803212851 1999999999999999999999999999

251: 79641434262549800796812749 119047619047619047619047619 260830039525691699604743083 236220472047244094488188937 352941176470196078431372549

256: 390624999999999999999960898 311284046688715953307392607 348837209301937984496124031 1081003861003861003861003861 11534576923076923076923076923

261: 766283524904210727969348659 1908014885496183206106870229 1520912547528517110266121673 2992424242424242424242424242 7546792452452830188679245283

266: 3007481203007518796992481203 3333333295880149812734082397 10820895485074626865671641791 7397769516728620817843866171 37037037037037037037037037037

271: 31690036900369003690036900369 25735294117647055147058823529 29263003663003663003663003663 29197007299270072992700729927

"1 minute and 50s"