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Chowla numbers: Difference between revisions

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Chowla numbers (view source)

Revision as of 14:20, 25 May 2021

10,313 bytes added ,  3 years ago
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→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎{{header|Phix}}: added syntax colouring the hard way)
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=={{header|Phix}}==
<!--<lang Phix>function chowla(atom nphixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">chowla</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
return sum(factors(n))
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function sieve(integer limit)
<span style="color: #008080;">function</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- True denotes composite, false denotes prime.
-- Only interested in odd numbers >&gt;= 3</span>
sequence c = repeat(false,limit)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span>
for i=3 to floor(limit/3) by 2 do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
-- if not c[i] and chowla(i)==0 then
<span style="color: #000080;font-style:italic;">-- if not c[i] then --and chowla(see note belowi)==0 then</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (see note below)</span>
for j=3*i to limit by 2*i do
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">i</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">i</span> <span style="color: #008080;">do</span>
c[j] = true
<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return c
<span style="color: #008080;">return</span> <span style="color: #000000;">c</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
atom limit = 1e7, count = 1, pow10 = 100, t0 = time()
<span style="color: #004080;">atom</span> <span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pow10</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
sequence s = {}
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
for i=1 to 37 do
<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;">37</span> <span style="color: #008080;">do</span>
s &= chowla(i)
<span style="color: #000000;">s</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">chowla</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
printf(1,"chowla[1..37]: %v\n",{s})
<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;">"chowla[1..37]: %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">})</span>
s = sieve(limit)
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span>
for i=3 to limit by 2 do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
if not s[i] then count += 1 end if
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if i==pow10-1 then
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">==</span><span style="color: #000000;">pow10</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
printf(1,"Count of primes up to %,d = %,d\n", {pow10, count})
<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;">"Count of primes up to %,d = %,d\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">pow10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">})</span>
pow10 *= 10
<span style="color: #000000;">pow10</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
count = 0
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
limit = iff(machine_bits()=32?1.4e11:2.4e18)
<span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">32</span><span style="color: #0000FF;">?</span><span style="color: #000000;">1.4e11</span><span style="color: #0000FF;">:</span><span style="color: #000000;">2.4e18</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--limit = power(2,iff(machine_bits()=32?53:64)) -- (see note below)</span>
integer i=2
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span>
while true do
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
atom p = power(2,i-1)*(power(2,i)-1) -- perfect numbers must be of this form
<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</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: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</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: #000080;font-style:italic;">-- perfect numbers must be of this form</span>
if p>limit then exit end if
<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">></span><span style="color: #000000;">limit</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>
if chowla(p)==p-1 then
<span style="color: #008080;">if</span> <span style="color: #000000;">chowla</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
printf(1,"%,d is a perfect number\n", p)
<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;">"%,d is a perfect number\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
count += 1
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
i += 1
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
printf(1,"There are %d perfect numbers <= %,d\n",{count,limit})
<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;">"There are %d perfect numbers &lt;= %,d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">})</span>
?elapsed(time()-t0)</lang>
<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>
<!--</lang>-->
The use of chowla() in sieve() does not actually achieve anything other than slow it down, so I took it out.
{{out}}
Petelomax
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