Frobenius numbers: Difference between revisions
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m (→{{header|REXX}}: added a REXX stub.) |
m (→{{header|REXX}}: added the computer programming language REXX.) |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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<lang rexx>/*REXX program finds Frobenius numbers where the numbers are less than some number N. */ |
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<lang rexx></lang> |
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parse arg hi cols . /*obtain optional argument from the CL.*/ |
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if hi=='' | hi=="," then hi= 10000 /* " " " " " " */ |
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if cols=='' | cols=="," then cols= 10 /* " " " " " " */ |
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call genP /*build array of semaphores for primes.*/ |
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w= 10 /*width of a number in any column. */ |
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@Frob= ' Frobenius numbers that are < ' commas(hi) |
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if cols>0 then say ' index │'center(@Frob, 1 + cols*(w+1) ) |
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if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') |
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idx= 1 /*initialize the index of output lines.*/ |
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$= /*a list of Frobenius numbers (so far)*/ |
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do j=1; jp= j + 1 /*generate Frobenius numbers < HI */ |
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y= @.j * @.jp - @.j - @.jp |
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if y>= hi then leave |
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if cols==0 then iterate /*Build the list (to be shown later)? */ |
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c= commas(y) /*maybe add commas to the number. */ |
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$= $ right(c, max(w, length(c) ) ) /*add a Frobenius #──►list, allow big #*/ |
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if j//cols\==0 then iterate /*have we populated a line of output? */ |
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say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */ |
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idx= idx + cols /*bump the index count for the output*/ |
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end /*j*/ |
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if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ |
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say |
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say 'Found ' commas(j-1) @FROB |
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exit 0 /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */ |
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#=5; s.#= @.# **2 /*number of primes so far; prime². */ |
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/* [↓] generate more primes ≤ high.*/ |
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do j=@.#+2 by 2 to hi /*find odd primes from here on. */ |
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parse var j '' -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/ |
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if j// 3==0 then iterate /*" " " 3? */ |
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if j// 7==0 then iterate /*" " " 7? */ |
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/* [↑] the above five lines saves time*/ |
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do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/ |
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if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */ |
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end /*k*/ /* [↑] only process numbers ≤ √ J */ |
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#= #+1; @.#= j; s.#= j*j /*bump # Ps; assign next P; P squared*/ |
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end /*j*/; return</lang> |
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{{out|output|text= when using the default inputs:}} |
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<pre> |
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index │ Frobenius numbers that are < 10,000 |
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───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
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1 │ 1 7 23 59 119 191 287 395 615 839 |
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11 │ 1,079 1,439 1,679 1,931 2,391 3,015 3,479 3,959 4,619 5,039 |
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21 │ 5,615 6,395 7,215 8,447 9,599 |
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Found 25 Frobenius numbers that are < 10,000 |
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</pre> |
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=={{header|Ring}}== |
=={{header|Ring}}== |