Triangular numbers: Difference between revisions
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(Created Nim solution.) |
(Added Sidef) |
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2: { 231205.405565 5431.99993865 893.442456752 } |
2: { 231205.405565 5431.99993865 893.442456752 } |
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1: { 5393607.15814 44355.7773766 4321 } |
1: { 5393607.15814 44355.7773766 4321 } |
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</pre> |
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=={{header|Sidef}}== |
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<syntaxhighlight lang="ruby">func pentatopic_root(x) { |
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(sqrt(5 + 4*sqrt(24*x + 1)) - 3)/2 |
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} |
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func polytopic (r, range) { |
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range.map {|n| binomial(n + r - 1, r) } |
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} |
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[ |
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2, 'triangular', 3, 'tetrahedral', 4, 'pentatopic', 12, '12-simplex' |
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].slices(2).each_2d {|r,label| |
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say "\nFirst 30 #{label} numbers:" |
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polytopic(r, ^30).slices(6).each{.join(' ').say} |
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} |
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for n in (7140, 21408696, 26728085384, 14545501785001) { |
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printf ("\nRoots of #{n}: |
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triangular-root: %s |
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tetrahedral-root: %s |
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pentatopic-root: %s\n", |
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polygonal_root(n,3), pyramidal_root(n,3), pentatopic_root(n)) |
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}</syntaxhighlight> |
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{{out}} |
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<pre> |
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First 30 triangular numbers: |
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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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First 30 tetrahedral numbers: |
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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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First 30 pentatopic numbers: |
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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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First 30 12-simplex numbers: |
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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-root: 119 |
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tetrahedral-root: 34 |
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pentatopic-root: 18.8766466159280066079017828266675662291603339398 |
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Roots of 21408696: |
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triangular-root: 6543 |
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tetrahedral-root: 503.56182697463651404819613028417773405650502954 |
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pentatopic-root: 149.060947375265867484387574884713368069543117436 |
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Roots of 26728085384: |
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triangular-root: 231205.405565255836957291031960694122304324644392 |
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tetrahedral-root: 5432 |
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pentatopic-root: 893.442456751684869888466211529245370387840101701 |
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Roots of 14545501785001: |
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triangular-root: 5393607.1581451723164973047246554846079685622181 |
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tetrahedral-root: 44355.7773840732560526209168894228874431786835756 |
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pentatopic-root: 4321 |
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</pre> |
</pre> |
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