Sylvester's sequence: Difference between revisions
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(→{{header|Python}}: Added a functionally composed solution in Python.) |
(→{{header|REXX}}: added the computer programming language REXX.) |
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Sum of the reciprocals of first 10 elements: 0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999635</pre> |
Sum of the reciprocals of first 10 elements: 0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999635</pre> |
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=={{header|REXX}}== |
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<lang rexx>/*REXX pgm finds/displays the Sylvester's sequence and the sum of the their reciprocals.*/ |
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parse arg n . /*obtain optional argument from the CL.*/ |
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if n=='' | n=="," then n= 10 /*Not specified? Then use the default.*/ |
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numeric digits max(9, 2**(n-7)*13 + 1) /*calculate how many dec. digs we need.*/ |
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@.0= 2 /*the value of the 1st Sylvester number*/ |
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$= 0 |
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do j=0 for n; jm= j - 1 /*calculate the Sylvester sequence. */ |
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if j>0 then @.j= @.jm**2 - @.jm + 1 /*calculate a Sylvester sequence num.*/ |
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say 'Sylvester('j") ──► " @.j /*display the Sylvester index & number.*/ |
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$= $ + 1 / @.j /*add its reciprocal to the recip. sum.*/ |
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end /*j*/ |
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say |
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numeric digits digits()-1 |
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say 'sum of the first ' n " reciprocals using" digits() 'decimal digits: ' $ / 1</lang> |
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{{out|output|text= when using the default inputs:}} |
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<pre> |
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Sylvester(0) ──► 2 |
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Sylvester(1) ──► 3 |
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Sylvester(2) ──► 7 |
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Sylvester(3) ──► 43 |
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Sylvester(4) ──► 1807 |
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Sylvester(5) ──► 3263443 |
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Sylvester(6) ──► 10650056950807 |
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Sylvester(7) ──► 113423713055421844361000443 |
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Sylvester(8) ──► 12864938683278671740537145998360961546653259485195807 |
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Sylvester(9) ──► 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443 |
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sum of the first 10 reciprocals using 104 decimal digits: 1 |
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</pre> |
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=={{header|Wren}}== |
=={{header|Wren}}== |