Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,62 +1,67 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- [join_by(fmt)]</span>
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<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>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">maxDigits</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10</span><span style="color: #0000FF;">:</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">pps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">()</span>
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with javascript_semantics
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requires("1.0.2") -- [join_by(fmt)]
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atom t0 = time()
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constant maxDigits = iff(platform()=JS?10:12)
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integer pps = new_dict()
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">getPerfectPowers</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">hi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">imax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hi</span><span style="color: #0000FF;">))</span>
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<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;">imax</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
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<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">hi</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>
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<span style="color: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pps</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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procedure getPerfectPowers(integer maxExp)
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atom hi = power(10, maxExp), t1 = time()+1
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integer imax = floor(sqrt(hi))
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for i=2 to imax do
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atom p = i
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while true do
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p *= i
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if p>=hi then exit end if
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setd(p,true,pps)
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end while
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if time()>t1 then
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progress("getting perfect powers, %d/%d\r",{i,imax})
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t1 = time()+1
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end if
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end for
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progress("")
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end procedure
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<span style="color: #008080;">function</span> <span style="color: #000000;">get_achilles</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">minExp</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">lo10</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">minExp</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">hi10</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">bmax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hi10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)),</span>
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<span style="color: #000000;">amax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hi10</span><span style="color: #0000FF;">))</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">achilles</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">bmax</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">b3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">amax</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b3</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">hi10</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>
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<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">lo10</span> <span style="color: #008080;">then</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pps</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">achilles</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">p</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #000000;">achilles</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">unique</span><span style="color: #0000FF;">(</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">achilles</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function get_achilles(integer minExp, maxExp)
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atom lo10 = power(10,minExp),
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hi10 = power(10,maxExp)
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integer bmax = floor(power(hi10,1/3)),
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amax = floor(sqrt(hi10))
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sequence achilles = {}
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for b=2 to bmax do
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atom b3 = b * b * b
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for a=2 to amax do
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atom p = b3 * a * a
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if p>=hi10 then exit end if
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if p>=lo10 then
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integer node = getd_index(p,pps)
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if node=NULL then
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achilles &= p
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end if
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end if
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end for
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end for
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achilles = unique(achilles)
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return achilles
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end function
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<span style="color: #000000;">getPerfectPowers</span><span style="color: #0000FF;">(</span><span style="color: #000000;">maxDigits</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">achilles</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_achilles</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
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getPerfectPowers(maxDigits)
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<span style="color: #008080;">function</span> <span style="color: #000000;">strong_achilles</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">totient</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_eq</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">gcd</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">n</span><span style="color: #0000FF;">}),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">totient</span><span style="color: #0000FF;">,</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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sequence achilles = get_achilles(1,5),
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a = join_by(achilles[1..50],1,10," ",fmt:="%4d")
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printf(1,"First 50 Achilles numbers:\n%s\n",{a})
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">50</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">sa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">,</span><span style="color: #000000;">strong_achilles</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">30</span><span style="color: #0000FF;">],</span>
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<span style="color: #000000;">ssa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%5d"</span><span style="color: #0000FF;">)</span>
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function strong_achilles(integer n)
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integer totient = sum(sq_eq(apply(true,gcd,{tagset(n),n}),1))
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return find(totient,achilles)
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end function
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<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;">"First 50 Achilles numbers:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">})</span>
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<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;">"First 30 strong Achilles numbers:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">ssa</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">maxDigits</span> <span style="color: #008080;">do</span>
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<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;">"Achilles numbers with %d digits:%d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_achilles</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: #000000;">d</span><span style="color: #0000FF;">))})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<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>
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<!--
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progress("filtering strong achilles...")
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sequence sa = filter(achilles,strong_achilles)[1..30],
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ssa = join_by(sa,1,10," ",fmt:="%5d")
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progress("")
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printf(1,"First 30 strong Achilles numbers:\n%s\n",{ssa})
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for d=2 to maxDigits do
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printf(1,"Achilles numbers with %d digits:%d\n",{d,length(get_achilles(d-1,d))})
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end for
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?elapsed(time()-t0)
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