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Permuted multiples: Difference between revisions

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Permuted multiples (view source)

Revision as of 18:21, 17 August 2021

673 bytes added ,  2 years ago
m
→‎{{header|Phix}}: multiple of 3 step 3
(Add Factor)
m (→‎{{header|Phix}}: multiple of 3 step 3)
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=={{header|Phix}}==
Maintain a limit (n10) and bump the iteration whenever *6 increases the number of digits, which (as [was] shown) cuts the number of iterations by a factor of nearly thirteen and a half times (as in eg [as was] 67 iterations instead of 900 to find nothing in 100..1,000). SomeoneAlso as noted on Projectthe Eulertalk notedpage, since sum(digits(3n)) is a multiple of 3 and it uses the answersame mustdigits "obviously"as n, then sum(digits(n)) will also be athe very same multiple of 93 and hence n must (also) be divisible by 3, notso clearwe whycan tostart meeach butlonger-digits theiteration commentedon out10^k+2 code(since worksremainder(10^k,3) fineis tooalways 1) and wouldemploy bea anotherstep nineof 3, and enjoy a better than 40-fold speedupoverall reduction in iterations.
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">13</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n10</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">steps</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">6</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">n10</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;">"Nothing less than %,d (%,d steps)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nsteps</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span>
<span style="color: #000080;font-style:italic;">-- n = n10+(9-remainder(n10,9))</span>
<span style="color: #000000;">n10</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
<span style="color: #000000;">steps</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">else</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #000080;font-style:italic;">-- (to test after loop)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ins</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">i</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">7</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: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">13</span>
<span style="color: #000080000000;font-">steps</span> <span style="color:italic #0000FF;">-- +=</span> <span n +style="color: 9#000000;">1</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>
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{{out}}
<pre>
Nothing less than 10 (20 steps)
Nothing less than 100 (172 steps)
Nothing less than 1,000 (16722 steps)
Nothing less than 10,000 (1,667222 steps)
Nothing less than 100,000 (162,667222 steps)
Smallest positive integer n for which (12..6)*n contain the same digits:
n = 142857
2 x n = 285714
Petelomax
7,805

edits

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