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Sequence: nth number with exactly n divisors: Difference between revisions

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Sequence: nth number with exactly n divisors (view source)

Revision as of 17:06, 11 June 2021

33,343 bytes added ,  2 years ago
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Certainly not the fastest way to do it, hence the relatively small limit of 24, which takes less than 0.4s,<br>
whereas a limit of 25 would need to invoke factors() 52 million times which would no doubt take a fair while.
<!--<lang Phix>constant LIMIT = 24(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
include mpfr.e
<span style="color: #008080;">constant</span> <span style="color: #000000;">LIMIT</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">24</span>
mpz z = mpz_init()
<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: #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>
sequence fn = 1&repeat(0,LIMIT-1)
integer k = 1
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fn</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;">LIMIT</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">fn</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;">1</span>
printf(1,"The first %d terms in the sequence are:\n",LIMIT)
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
for i=1 to LIMIT do
<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 first %d terms in the sequence are:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">LIMIT</span><span style="color: #0000FF;">)</span>
if is_prime(i) then
<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;">LIMIT</span> <span style="color: #008080;">do</span>
mpz_ui_pow_ui(z,get_prime(i),i-1)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
printf(1,"%2d : %s\n",{i,mpz_get_str(z)})
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</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>
else
<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;">"%2d : %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</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>
while fn[i]<i do
<span style="color: #008080;">else</span>
k += 1
<span style="color: #008080;">while</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">i</span> <span style="color: #008080;">do</span>
integer l = length(factors(k,1))
<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
if l<=LIMIT and fn[l]<l then
<span style="color: #004080;">integer</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: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
fn[l] = iff(fn[l]+1<l?fn[l]+1:k)
<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">LIMIT</span> <span style="color: #008080;">and</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">l</span> <span style="color: #008080;">then</span>
end if
<span style="color: #000000;">fn</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: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</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: #0000FF;"><</span><span style="color: #000000;">l</span><span style="color: #0000FF;">?</span><span style="color: #000000;">fn</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: #0000FF;">:</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
printf(1,"%2d : %d\n",{i,fn[i]})
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end if
<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;">"%2d : %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]})</span>
end for</lang>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</lang>-->
{{out}}
<pre>
Line 1,142 ⟶ 1,145:
===cheating slightly===
No real patterns that I could see here, but you can still identify and single out the troublemakers (of which there are about 30).
<!--<lang Phix>include mpfr.e(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
atom t0 = time()
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
constant LIMIT = 100
<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>
include mpfr.e
<span style="color: #008080;">constant</span> <span style="color: #000000;">LIMIT</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span>
include primes.e
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
mpz z = mpz_init(),
<span style="color: #008080;">include</span> <span style="color: #000000;">primes</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
p = mpz_init()
<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>
string mz
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
sequence fn = 1&repeat(0,LIMIT-1), dx
<span style="color: #004080;">string</span> <span style="color: #000000;">mz</span>
integer k = 1, idx, p1, p2
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fn</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;">LIMIT</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;">;</span> <span style="color: #000000;">fn</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;">1</span>
printf(1,"The first %d terms in the sequence are:\n",LIMIT)
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">idx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p2</span>
for i=1 to LIMIT do
<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 first %d terms in the sequence are:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">LIMIT</span><span style="color: #0000FF;">)</span>
if is_prime(i) or i=1 then
<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;">LIMIT</span> <span style="color: #008080;">do</span>
mpz_ui_pow_ui(z,get_prime(i),i-1)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</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>
mz = mpz_get_str(z)
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</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>
else
<span style="color: #000000;">mz</span> <span style="color: #0000FF;">=</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>
sequence f = prime_factors(i,1)
<span style="color: #008080;">else</span>
if length(f)=2 and f[1]=2 and f[2]>7 then
<span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prime_factors</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>
mz = sprintf("%d",power(2,f[2]-1)*get_prime(i+1))
<span style="color: #008080;">if</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: #000000;">2</span> <span style="color: #008080;">and</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: #008080;">and</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]></span><span style="color: #000000;">7</span> <span style="color: #008080;">then</span>
elsif length(f)=2 and f[1]>2 then
<span style="color: #000000;">mz</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: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">get_prime</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>
if f[1]=f[2] then
<span style="color: #008080;">elsif</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: #000000;">2</span> <span style="color: #008080;">and</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: #008080;">then</span>
mz = sprintf("%d",power(f[1]*get_prime(f[1]+2),f[1]-1))
<span style="color: #008080;">if</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;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
else -- deal with some tardy ones...
<span style="color: #000000;">mz</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: #7060A8;">power</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: #7060A8;">get_prime</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: #000000;">f</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>
dx = {15,21,33,35,39,51,55,57,65,69,77,85,87,91,93,95}; idx = find(i,dx)
<span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- deal with some tardy ones...</span>
p1 = { 3, 2, 2, 5, 2, 2, 2, 2, 2, 2, 7, 2, 2, 7, 2, 2}[idx]
<span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">21</span><span style="color: #0000FF;">,</span><span style="color: #000000;">33</span><span style="color: #0000FF;">,</span><span style="color: #000000;">35</span><span style="color: #0000FF;">,</span><span style="color: #000000;">39</span><span style="color: #0000FF;">,</span><span style="color: #000000;">51</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">,</span><span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">65</span><span style="color: #0000FF;">,</span><span style="color: #000000;">69</span><span style="color: #0000FF;">,</span><span style="color: #000000;">77</span><span style="color: #0000FF;">,</span><span style="color: #000000;">85</span><span style="color: #0000FF;">,</span><span style="color: #000000;">87</span><span style="color: #0000FF;">,</span><span style="color: #000000;">91</span><span style="color: #0000FF;">,</span><span style="color: #000000;">93</span><span style="color: #0000FF;">,</span><span style="color: #000000;">95</span><span style="color: #0000FF;">};</span> <span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">)</span>
p2 = { 5,15,29, 6,35,49,34,56,45,69, 7,65,88, 7,94,77}[idx]
<span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
mpz_ui_pow_ui(z,p1,f[2]-1)
<span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">29</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">35</span><span style="color: #0000FF;">,</span><span style="color: #000000;">49</span><span style="color: #0000FF;">,</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">56</span><span style="color: #0000FF;">,</span><span style="color: #000000;">45</span><span style="color: #0000FF;">,</span><span style="color: #000000;">69</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">65</span><span style="color: #0000FF;">,</span><span style="color: #000000;">88</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">94</span><span style="color: #0000FF;">,</span><span style="color: #000000;">77</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
mpz_ui_pow_ui(p,get_prime(p2),f[1]-1)
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
mpz_mul(z,z,p)
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2</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;">1</span><span style="color: #0000FF;">)</span>
mz = mpz_get_str(z)
<span style="color: #7060A8;">mpz_mul</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;">p</span><span style="color: #0000FF;">)</span>
end if
<span style="color: #000000;">mz</span> <span style="color: #0000FF;">=</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>
elsif (length(f)=3 and i>50) or (length(f)=4 and (f[1]=3 or f[4]>7)) then
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if i=99 then -- (oops, messed that one up!)
<span style="color: #008080;">elsif</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: #000000;">3</span> <span style="color: #008080;">and</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">></span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">or</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: #000000;">4</span> <span style="color: #008080;">and</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;">3</span> <span style="color: #008080;">or</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]></span><span style="color: #000000;">7</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">then</span>
mz = sprintf("%d",4*power(3,10)*31*31)
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">99</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (oops, messed that one up!)</span>
elsif i=63 then -- (and another!)
<span style="color: #000000;">mz</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;">4</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">31</span><span style="color: #0000FF;">*</span><span style="color: #000000;">31</span><span style="color: #0000FF;">)</span>
mz = sprintf("%d",power(2,8)*power(5,6))
<span style="color: #008080;">elsif</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">63</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (and another!)</span>
else
<span style="color: #000000;">mz</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: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">))</span>
dx = {52,66,68,70,75,76,78,92,98,81,88}; idx = find(i,dx)
<span p1 style="color: { 7, 3, 1, 5, 3, 5, 5,13, 3,35,35}[idx]#008080;">else</span>
<span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">52</span><span style="color: #0000FF;">,</span><span style="color: #000000;">66</span><span style="color: #0000FF;">,</span><span style="color: #000000;">68</span><span style="color: #0000FF;">,</span><span style="color: #000000;">70</span><span style="color: #0000FF;">,</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">76</span><span style="color: #0000FF;">,</span><span style="color: #000000;">78</span><span style="color: #0000FF;">,</span><span style="color: #000000;">92</span><span style="color: #0000FF;">,</span><span style="color: #000000;">98</span><span style="color: #0000FF;">,</span><span style="color: #000000;">81</span><span style="color: #0000FF;">,</span><span style="color: #000000;">88</span><span style="color: #0000FF;">};</span> <span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">)</span>
p2 = { 1, 2, 1, 4, 4, 1, 2, 1, 1, 2, 1}[idx]
<span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</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> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">35</span><span style="color: #0000FF;">,</span><span style="color: #000000;">35</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
mpz_ui_pow_ui(z,2,f[$]-1)
<span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
mpz_ui_pow_ui(p,p1,p2)
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[$]-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
mpz_mul(z,z,p)
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">)</span>
p1 = {13,37, 4, 9,34,22,19,12, 4,11,13}[idx]
<span style="color: #7060A8;">mpz_mul</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;">p</span><span style="color: #0000FF;">)</span>
p2 = { 1, 1, 3, 1, 2, 1, 1, 1, 6, 2, 1}[idx]
<span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">37</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">22</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
mpz_ui_pow_ui(p,get_prime(p1),p2)
<span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</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: #000000;">3</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: #000000;">1</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: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
mpz_mul(z,z,p)
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">)</span>
mz = mpz_get_str(z)
<span style="color: #7060A8;">mpz_mul</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;">p</span><span style="color: #0000FF;">)</span>
end if
<span style="color: #000000;">mz</span> <span style="color: #0000FF;">=</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>
else
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
while fn[i]<i do
<span k +style="color: 1#008080;">else</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">i</span> <span style="color: #008080;">do</span>
integer l = length(factors(k,1))
<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
if l<=LIMIT and fn[l]<l then
<span style="color: #004080;">integer</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: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
fn[l] = iff(fn[l]+1<l?fn[l]+1:k)
<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">LIMIT</span> <span style="color: #008080;">and</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">l</span> <span style="color: #008080;">then</span>
end if
<span style="color: #000000;">fn</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: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</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: #0000FF;"><</span><span style="color: #000000;">l</span><span style="color: #0000FF;">?</span><span style="color: #000000;">fn</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: #0000FF;">:</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
mz = sprintf("%d",fn[i])
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end if
<span style="color: #000000;">mz</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;">fn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
printf(1,"%3d : %s\n",{i,mz})
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for
<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;">"%3d : %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mz</span><span style="color: #0000FF;">})</span>
printf(1,"completed in %s\n",{elapsed(time()-t0)})</lang>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"completed in %s\n"</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>
<!--</lang>-->
{{out}}
<pre>
Petelomax
7,805

edits

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