Jordan-Pólya numbers: Difference between revisions

Line 425:

function decompose(atom jp)

atom <span~~ style~~="color~~: ~~#000000~~;">~~jp0 = jp

--

-- Subtract prime powers of factorials off the prime powers of the jp number,

⚫

sequence f = ~~factorials_le~~(jp)

-- only for factorials that have the same high prime factor as the remainder,

⚫

~~while~~ ~~true~~ do

-- and only putting things back on the todo list if still viable.

⚫

~~string~~ ~~res~~ = ""

-- Somewhat slowish, but at least it /is/ very thorough.

⚫

for i=length(f) to 2 by -1 do

--

⚫

~~atom~~ fi = f[i]

if ~~remainder~~(jp,fi)~~=0 then~~

sequence p = prime_powers(jp)

jp /= fi

integer lp = length(p),

if ~~length~~(~~res~~) ~~then~~ ~~res~~ &= " * " <span~~ style~~="color~~: ~~#008080~~;">~~end~~ ~~<span~~ ~~style="color:~~ ~~#008080;">if

mp = p[lp][1], -- (max prime factor)

~~res~~ &= ~~sprintf~~("~~%d!~~",i)

hf = get_prime(lp+1)-1 -- (high factorial)

~~integer~~ fc = 0

assert(mp = get_prime(lp))

~~while~~ ~~remainder~~(jp,fi)=0 <span~~ style~~="color~~: ~~#008080;">do

sequence ap = get_primes_le(mp), -- (all primes)

jp /= fi

fs = apply(tagset(hf),factorial),

fc += 1

fp = apply(fs,prime_powers),

⚫

pf = repeat(0,hf), -- (powers of factorials)

⚫

end while

if fc ~~then~~

todo = {{p,pf}},

~~res~~ &= ~~sprintf("^%d"~~,~~fc+1)~~

seen = {},

result = {}

while length(todo) do

{{p,pf},todo} = {todo[1],todo[2..$]}

for fdx,fpi in fp from 2 do

if fpi[$][1] = p[$][1] then -- same max prime factor

⚫

bool ok = true

for j,fpij in fpi do

if fpij[2]>p[find(fpij[1],ap)][2] then

-- this factorial ain't a factor

ok = false

exit

end if

end for

⚫

if ok then

-- reduce & trim the remaining prime powers:

⚫

sequence pnxt = deep_copy(p)

for j,fpij in fpi do

pnxt[find(fpij[1],ap)][2] -= fpij[2]

end for

while length(pnxt) and pnxt[$][2]=0 do

pnxt = pnxt[1..$-1]

⚫

end while

sequence fnxt = deep_copy(pf)

fnxt[fdx] += 1 -- **one** extra factorial power

if length(pnxt) then

bool bBad = false

for i=2 to length(pnxt) do

if pnxt[i][2]>pnxt[i-1][2] then

-- ie/eg you cannot ever knock a 7! or above off

-- if there ain't enough 5 (and 3 and 2) avail.

bBad = true

exit

end if

end for

if not bBad

and not find({pnxt,fnxt},seen) then

seen = append(seen,{pnxt,fnxt})

todo = append(todo,{pnxt,fnxt})

end if

else

result = append(result,fnxt)

end if

⚫

if jp=1 ~~then~~ ~~return~~ ~~res~~ ~~end~~ if

end for

f = ~~<span~~ ~~style="color:~~ ~~#000000;">f<span~~ ~~style="color:~~ ~~#0000FF;">[<span~~ ~~style="color:~~ ~~#000000;">1..-2]~~

end while

jp = ~~jp0~~

result = reverse(sort(apply(result,reverse))[$])

~~end~~ ~~while~~

string res = ""

⚫

for i=length(result) to 1 by -1 do

if result[i] then

if length(res) then res &= " * " end if

res &= sprintf("%d!",i)

⚫

if result[i]>1 then

res &= sprintf("^%d",result[i])

end if

end for

return res

end function

Line 456:

Line 507:

{length(r),join_by(r[1..50],1,10," ",fmt:="%4d")})

printf(1,"The largest under 100 million: %,d\n",r[abs(binary_search(1e8,r))-1])

for i in {100,800,1800,2800,3800} do

for i in {100,800,1050,1800,2800,3800} do

printf(1,"The %d%s is %,d = %s\n",{i,ord(i),r[i],decompose(r[i])})

end for

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Line 514:

<pre>

3887 Jordan-Polya numbers found, the first 50 are:

1 2 4 6 8 12 16 24 32 36

48 64 72 96 120 128 144 192 216 240

256 288 384 432 480 512 576 720 768 864

960 1024 1152 1296 1440 1536 1728 1920 2048 2304

2592 2880 3072 3456 3840 4096 4320 4608 5040 5184

The largest under 100 million: 99,532,800

The 100th is 92,160 = 6! * 2!^7

~~The 800th is 18~~,345,885,~~696~~ = 4!^7 * 2!^2

The 800th is 18,345,885,696 = 4!^7 * 2!^2

The 1050th is 139,345,920,000 = 8! * 5!^3 * 2!

The 1800th is 9,784,472,371,200 = 6!^2 * 4!^2 * 2!^15

The 2800th is 439,378,587,648,000 = 14! * 7!

The 3800th is 7,213,895,789,838,336 = 4!^8 * 2!^16

"0.3s"

"1.5s"

</pre>

Some 80%-90% of the time is now spent in the decomposing phase.

Actually slightly faster under pwa/p2js than it is on desktop/Phix.

=={{header|Wren}}==

@@ Line 425: / Line 425: @@
  <span style="color: #008080;">function</span> <span style="color: #000000;">decompose</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">jp</span><span style="color: #0000FF;">)</span>
-     <span style="color: #004080;">atom</span> <span style="color: #000000;">jp0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">jp</span>
+     <span style="color: #000080;font-style:italic;">--
+     -- Subtract prime powers of factorials off the prime powers of the jp number,
-     <span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">factorials_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">jp</span><span style="color: #0000FF;">)</span>
+     -- only for factorials that have the same high prime factor as the remainder,
-     <span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
+     -- and only putting things back on the todo list if still viable.
-         <span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
+     -- Somewhat slowish, but at least it /is/ very thorough.
-         <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</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>
-             <span style="color: #004080;">atom</span> <span style="color: #000000;">fi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
-             <span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">jp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fi</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prime_powers</span><span style="color: #0000FF;">(</span><span style="color: #000000;">jp</span><span style="color: #0000FF;">)</span>
-                 <span style="color: #000000;">jp</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">fi</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">lp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</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;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">" * "</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+             <span style="color: #000000;">mp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lp</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span>  <span style="color: #000080;font-style:italic;">-- (max prime factor)</span>
-                 <span style="color: #000000;">res</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;">i</span><span style="color: #0000FF;">)</span>
+             <span style="color: #000000;">hf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- (high factorial)</span>
-                 <span style="color: #004080;">integer</span> <span style="color: #000000;">fc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
+     <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lp</span><span style="color: #0000FF;">))</span>
-                 <span style="color: #008080;">while</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">jp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fi</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">ap</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mp</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (all primes)</span>
-                     <span style="color: #000000;">jp</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">fi</span>
+              <span style="color: #000000;">fs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hf</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">),</span>
-                     <span style="color: #000000;">fc</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
+              <span style="color: #000000;">fp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fs</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">prime_powers</span><span style="color: #0000FF;">),</span>
+              <span style="color: #000000;">pf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hf</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (powers of factorials)</span>
-                 <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
-                 <span style="color: #008080;">if</span> <span style="color: #000000;">fc</span> <span style="color: #008080;">then</span>
+              <span style="color: #000000;">todo</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pf</span><span style="color: #0000FF;">}},</span>
-                     <span style="color: #000000;">res</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;">fc</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+              <span style="color: #000000;">seen</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
+              <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
+     <span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">todo</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
+         <span style="color: #0000FF;">{{</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pf</span><span style="color: #0000FF;">},</span><span style="color: #000000;">todo</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">todo</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">todo</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]}</span>
+         <span style="color: #008080;">for</span> <span style="color: #000000;">fdx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fpi</span> <span style="color: #008080;">in</span> <span style="color: #000000;">fp</span> <span style="color: #008080;">from</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">fpi</span><span style="color: #0000FF;">[$][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[$][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- same max prime factor</span>
+                 <span style="color: #004080;">bool</span> <span style="color: #000000;">ok</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
+                 <span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fpij</span> <span style="color: #008080;">in</span> <span style="color: #000000;">fpi</span> <span style="color: #008080;">do</span>
+                     <span style="color: #008080;">if</span> <span style="color: #000000;">fpij</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]></span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fpij</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">ap</span><span style="color: #0000FF;">)][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
+                         <span style="color: #000080;font-style:italic;">-- this factorial ain't a factor</span>
+                         <span style="color: #000000;">ok</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</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: #000000;">ok</span> <span style="color: #008080;">then</span>
+                     <span style="color: #000080;font-style:italic;">-- reduce & trim the remaining prime powers:</span>
+                     <span style="color: #004080;">sequence</span> <span style="color: #000000;">pnxt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
+                     <span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fpij</span> <span style="color: #008080;">in</span> <span style="color: #000000;">fpi</span> <span style="color: #008080;">do</span>
+                         <span style="color: #000000;">pnxt</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fpij</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">ap</span><span style="color: #0000FF;">)][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">fpij</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
+                     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+                     <span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pnxt</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">pnxt</span><span style="color: #0000FF;">[$][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
+                         <span style="color: #000000;">pnxt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pnxt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</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;">fnxt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pf</span><span style="color: #0000FF;">)</span>
+                     <span style="color: #000000;">fnxt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">fdx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- **one** extra factorial power</span>
+                     <span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pnxt</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
+                         <span style="color: #004080;">bool</span> <span style="color: #000000;">bBad</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;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pnxt</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
+                             <span style="color: #008080;">if</span> <span style="color: #000000;">pnxt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]></span><span style="color: #000000;">pnxt</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;">2</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
+                                 <span style="color: #000080;font-style:italic;">-- ie/eg you cannot ever knock a 7! or above off
+                                 --  if there ain't enough 5 (and 3 and 2) avail.</span>
+                                 <span style="color: #000000;">bBad</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</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;">bBad</span>
+                         <span style="color: #008080;">and</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">({</span><span style="color: #000000;">pnxt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fnxt</span><span style="color: #0000FF;">},</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
+                             <span style="color: #000000;">seen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">pnxt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fnxt</span><span style="color: #0000FF;">})</span>
+                             <span style="color: #000000;">todo</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">todo</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">pnxt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fnxt</span><span style="color: #0000FF;">})</span>
+                         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+                     <span style="color: #008080;">else</span>
+                         <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fnxt</span><span style="color: #0000FF;">)</span>
+                     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
                  <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
              <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-             <span style="color: #008080;">if</span> <span style="color: #000000;">jp</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: #000000;">res</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: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
-         <span style="color: #000000;">jp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">jp0</span>
+     <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">))[$])</span>
-     <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">)</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: #008080;">if</span> <span style="color: #000000;">result</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: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">" * "</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+             <span style="color: #000000;">res</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;">i</span><span style="color: #0000FF;">)</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">result</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: #008080;">then</span>
+                 <span style="color: #000000;">res</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;">result</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
+             <span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">return</span> <span style="color: #000000;">res</span>
  <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
@@ Line 456: / Line 507: @@
           <span style="color: #0000FF;">{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</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>
  <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;">"The largest under 100 million: %,d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">binary_search</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1e8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">))-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
- <span style="color: #008080;">for</span> <span style="color: #000000;">i</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3800</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">i</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1050</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3800</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</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;">"The %d%s is %,d = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">),</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">decompose</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])})</span>
  <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
@@ Line 463: / Line 514: @@
 {{out}}
 <pre>
+Jordan-Polya numbers found, the first 50 are:
- Jordan-Polya numbers found, the first 50 are:
+2    4    6    8   12   16   24   32   36
-    2    4    6    8   12   16   24   32   36
+64   72   96  120  128  144  192  216  240
-   64   72   96  120  128  144  192  216  240
+288  384  432  480  512  576  720  768  864
-  288  384  432  480  512  576  720  768  864
+1024 1152 1296 1440 1536 1728 1920 2048 2304
- 1024 1152 1296 1440 1536 1728 1920 2048 2304
+2880 3072 3456 3840 4096 4320 4608 5040 5184
- 2880 3072 3456 3840 4096 4320 4608 5040 5184
+The largest under 100 million: 99,532,800
-The largest under 100 million: 99,532,800
+The 100th is 92,160 = 6! * 2!^7
-The 100th is 92,160 = 6! * 2!^7
-The 800th is 18,345,885,696 = 4!^7 * 2!^2
+The 800th is 18,345,885,696 = 4!^7 * 2!^2
+The 1050th is 139,345,920,000 = 8! * 5!^3 * 2!
-The 1800th is 9,784,472,371,200 = 6!^2 * 4!^2 * 2!^15
+The 1800th is 9,784,472,371,200 = 6!^2 * 4!^2 * 2!^15
-The 2800th is 439,378,587,648,000 = 14! * 7!
+The 2800th is 439,378,587,648,000 = 14! * 7!
-The 3800th is 7,213,895,789,838,336 = 4!^8 * 2!^16
+The 3800th is 7,213,895,789,838,336 = 4!^8 * 2!^16
-"0.3s"
+"1.5s"
 </pre>
+Some 80%-90% of the time is now spent in the decomposing phase.
-Actually slightly faster under pwa/p2js than it is on desktop/Phix.
 =={{header|Wren}}==