Sisyphus sequence: Difference between revisions
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=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<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>
<span style="color: #008080;">constant</span> <span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e8</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sisyphus</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;">under250</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reinstate</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;">250</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: #004080;">integer</span> <span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">specific</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000</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;">m</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">next</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">next</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">np</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">next</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">250</span> <span style="color: #008080;">then</span> <span style="color: #000000;">under250</span><span style="color: #0000FF;">[</span><span style="color: #000000;">next</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">100</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sisyphus</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">next</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">100</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"The first 100 members of the Sisyphus sequence are:\n%s\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sisyphus</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;">"%3d"</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">specific</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%,13d%s member is: %,13d and highest prime needed: %,11d\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">then</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">largest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">under250</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">);</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">specific</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<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;">"\nThese numbers under 250 do not occur in the first %,d terms:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</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;">" %v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">find_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">under250</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;">"\nThese numbers under 250 occur the most in the first %,d terms:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</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;">" %v all occur %d times.\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">find_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">under250</span><span style="color: #0000FF;">),</span><span style="color: #000000;">m</span><span style="color: #0000FF;">})</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>
<!--</syntaxhighlight>-->
{{out}}
<pre>
The first 100 members of the Sisyphus sequence are:
1 3 6 3 8 4 2 1 8 4
2 1 12 6 3 16 8 4 2 1
18 9 28 14 7 30 15 44 22 11
42 21 58 29 70 35 78 39 86 43
96 48 24 12 6 3 62 31 92 46
23 90 45 116 58 29 102 51 130 65
148 74 37 126 63 160 80 40 20 10
5 106 53 156 78 39 146 73 182 91
204 102 51 178 89 220 110 55 192 96
48 24 12 6 3 142 71 220 110 55
1,000th member is: 990 and highest prime needed: 2,273
10,000th member is: 24,975 and highest prime needed: 30,713
100,000th member is: 265,781 and highest prime needed: 392,111
1,000,000th member is: 8,820,834 and highest prime needed: 4,761,697
10,000,000th member is: 41,369,713 and highest prime needed: 55,900,829
100,000,000th member is: 1,179,614,168 and highest prime needed: 640,692,323
These numbers under 250 do not occur in the first 100,000,000 terms:
{36,72,97,107,115,127,144,167,194,211,214,230,232}
These numbers under 250 occur the most in the first 100,000,000 terms:
{7,14,28} all occur 7 times.
"12.8s"
</pre>
===Extreme stretch (just a note about)===
Knowing that jp(77,534,485,877)=36, a crude extrapolation of the above figures suggests it would
need primes up to 570 billion, or about 30 billion of them, or at least 480GB of RAM, which is a
tad more than I have available on this machine... If, on the other hand, I could figure out how to
not need quite so much ram, it ''might'' be achievable in as little as between 4 and 28 hours...
=={{header|Python}}==
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