Triangular numbers: Difference between revisions
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(Added Algol 68) |
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tetrahedral-root : 44355.777376558433 |
tetrahedral-root : 44355.777376558433 |
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pentatopic -root : 4321.000000000000 |
pentatopic -root : 4321.000000000000 |
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</pre> |
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=={{header|Phix}}== |
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<!--<syntaxhighlight lang="phix">(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">t</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;">30</span><span style="color: #0000FF;">)</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">30</span> <span style="color: #008080;">do</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"The first 30 triangular numbers are:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</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;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%3d"</span><span style="color: #0000FF;">)})</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">30</span> <span style="color: #008080;">do</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"The first 30 tetrahedral numbers are:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</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;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">)})</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">30</span> <span style="color: #008080;">do</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"The first 30 pentatopic numbers are:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</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;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%5d"</span><span style="color: #0000FF;">)})</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">5</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">do</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">30</span> <span style="color: #008080;">do</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #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 30 12-simplex numbers are:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</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;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%10d"</span><span style="color: #0000FF;">)})</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">x</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">7140</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21408696</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">26728085384</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">14545501785001</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nRoots of %d:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">8</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> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%14s: %f\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"triangular"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">root</span><span style="color: #0000FF;">})</span> |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">temp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">27</span><span style="color: #0000FF;">)</span> |
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<span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">3</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">temp</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: #0000FF;">+</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">3</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">temp</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: #0000FF;">-</span> <span style="color: #000000;">1</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%14s: %f\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"tetrahedral"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">root</span><span style="color: #0000FF;">})</span> |
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<span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">24</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;">5</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: #0000FF;">/</span> <span style="color: #000000;">2</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%14s: %f\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"pentatopic"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">root</span><span style="color: #0000FF;">})</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<!--</syntaxhighlight>--> |
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{{out}} |
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<pre> |
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The first 30 triangular numbers are: |
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0 1 3 6 10 15 |
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21 28 36 45 55 66 |
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78 91 105 120 136 153 |
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171 190 210 231 253 276 |
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300 325 351 378 406 435 |
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The first 30 tetrahedral numbers are: |
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0 1 4 10 20 35 |
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56 84 120 165 220 286 |
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364 455 560 680 816 969 |
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1140 1330 1540 1771 2024 2300 |
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2600 2925 3276 3654 4060 4495 |
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The first 30 pentatopic numbers are: |
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0 1 5 15 35 70 |
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126 210 330 495 715 1001 |
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1365 1820 2380 3060 3876 4845 |
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5985 7315 8855 10626 12650 14950 |
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17550 20475 23751 27405 31465 35960 |
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The first 30 12-simplex numbers are: |
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0 1 13 91 455 1820 |
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6188 18564 50388 125970 293930 646646 |
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1352078 2704156 5200300 9657700 17383860 30421755 |
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51895935 86493225 141120525 225792840 354817320 548354040 |
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834451800 1251677700 1852482996 2707475148 3910797436 5586853480 |
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Roots of 7140: |
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triangular: 119.000000 |
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tetrahedral: 34.000000 |
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pentatopic: 18.876647 |
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Roots of 21408696: |
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triangular: 6543.000000 |
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tetrahedral: 503.561166 |
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pentatopic: 149.060947 |
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Roots of 26728085384: |
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triangular: 231205.405565 |
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tetrahedral: 5431.999939 |
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pentatopic: 893.442457 |
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Roots of 14545501785001: |
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triangular: 5393607.158145 |
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tetrahedral: 44355.777377 |
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pentatopic: 4321.000000 |
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</pre> |
</pre> |
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