Coprime triplets: Difference between revisions
(Added AppleScript.) |
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Found 36 coprime triplets up to 49 |
Found 36 coprime triplets up to 49 |
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</pre> |
</pre> |
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=={{header|AppleScript}}== |
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<lang applescript>on hcf(a, b) |
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repeat until (b = 0) |
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set x to a |
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set a to b |
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set b to x mod b |
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end repeat |
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if (a < 0) then return -a |
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return a |
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end hcf |
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on coprimeTriplets(max) |
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if (max < 3) then return {} |
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script o |
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property candidates : {} |
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property output : {1, 2} |
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end script |
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-- When repeatedly searching for lowest unused numbers, it's faster in |
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-- AppleScript to take numbers from a preset list of candidates which |
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-- grows shorter from at or near the low end as used numbers are removed |
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-- than it is to test increasing numbers of previous numbers each time |
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-- against a list that's growing longer with them. |
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-- Generate the list of candidates here. |
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repeat with i from 3 to max |
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set end of o's candidates to i |
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end repeat |
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set candidateCount to max - 2 |
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set {p1, p2} to o's output |
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set ok to true |
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repeat while (ok) -- While suitable coprimes found and candidates left. |
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repeat with i from 1 to candidateCount |
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set q to item i of o's candidates |
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set ok to ((hcf(p1, q) is 1) and (hcf(p2, q) is 1)) |
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if (ok) then -- q is coprime with both p1 and p2. |
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set end of o's output to q |
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set p1 to p2 |
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set p2 to q |
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-- Remove q from the candidate list. |
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set item i of o's candidates to missing value |
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set o's candidates to o's candidates's numbers |
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set candidateCount to candidateCount - 1 |
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set ok to (candidateCount > 0) |
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exit repeat |
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end if |
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end repeat |
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end repeat |
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return o's output |
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end coprimeTriplets |
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-- Task code: |
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return coprimeTriplets(49)</lang> |
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{{output}} |
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<lang applescript>{1, 2, 3, 5, 4, 7, 9, 8, 11, 13, 6, 17, 19, 10, 21, 23, 16, 15, 29, 14, 25, 27, 22, 31, 35, 12, 37, 41, 18, 43, 47, 20, 33, 49, 26, 45}</lang> |
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=={{header|Factor}}== |
=={{header|Factor}}== |
Revision as of 21:46, 30 April 2021
- Task
Find and show the smallest number which is coprime to the last two predecessors and has not yet appeared; a(1)=1, a(2)=2.
p and q are coprimes if they have no common factors other than 1.
Let p, q < 50
ALGOL 68
<lang algol68>BEGIN # find members of the coprime triplets sequence: starting from 1, 2 the #
# subsequent members are the lowest number coprime to the previous two # # that haven't appeared in the sequence yet # # iterative Greatest Common Divisor routine, returns the gcd of m and n # PROC gcd = ( INT m, n )INT: IF m = 0 THEN n ELSE INT a := ABS m, b := ABS n; WHILE b /= 0 DO INT new a = b; b := a MOD b; a := new a OD; a FI # gcd # ; # returns an array of the coprime triplets up to n # OP COPRIMETRIPLETS = ( INT n )[]INT: BEGIN [ 1 : n ]INT result; IF n > 0 THEN result[ 1 ] := 1; IF n > 1 THEN [ 1 : n ]BOOL used; used[ 1 ] := used[ 2 ] := TRUE; FOR i FROM 3 TO n DO used[ i ] := FALSE; result[ i ] := 0 OD; result[ 2 ] := 2; FOR i FROM 3 TO n DO INT p1 = result[ i - 1 ]; INT p2 = result[ i - 2 ]; BOOL found := FALSE; FOR j TO n WHILE NOT found DO IF NOT used[ j ] THEN found := gcd( p1, j ) = 1 AND gcd( p2, j ) = 1; IF found THEN used[ j ] := TRUE; result[ i ] := j FI FI OD OD FI FI; result END # COPRIMETRIPLETS # ; []INT cps = COPRIMETRIPLETS 49; INT printed := 0; FOR i TO UPB cps DO IF cps[ i ] /= 0 THEN print( ( whole( cps[ i ], -3 ) ) ); printed +:= 1; IF printed MOD 10 = 0 THEN print( ( newline ) ) FI FI OD; print( ( newline, "Found ", whole( printed, 0 ), " coprime triplets up to ", whole( UPB cps, 0 ), newline ) )
END</lang>
- Output:
1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45 Found 36 coprime triplets up to 49
AppleScript
<lang applescript>on hcf(a, b)
repeat until (b = 0) set x to a set a to b set b to x mod b end repeat if (a < 0) then return -a return a
end hcf
on coprimeTriplets(max)
if (max < 3) then return {} script o property candidates : {} property output : {1, 2} end script -- When repeatedly searching for lowest unused numbers, it's faster in -- AppleScript to take numbers from a preset list of candidates which -- grows shorter from at or near the low end as used numbers are removed -- than it is to test increasing numbers of previous numbers each time -- against a list that's growing longer with them. -- Generate the list of candidates here. repeat with i from 3 to max set end of o's candidates to i end repeat set candidateCount to max - 2 set {p1, p2} to o's output set ok to true repeat while (ok) -- While suitable coprimes found and candidates left. repeat with i from 1 to candidateCount set q to item i of o's candidates set ok to ((hcf(p1, q) is 1) and (hcf(p2, q) is 1)) if (ok) then -- q is coprime with both p1 and p2. set end of o's output to q set p1 to p2 set p2 to q -- Remove q from the candidate list. set item i of o's candidates to missing value set o's candidates to o's candidates's numbers set candidateCount to candidateCount - 1 set ok to (candidateCount > 0) exit repeat end if end repeat end repeat return o's output
end coprimeTriplets
-- Task code: return coprimeTriplets(49)</lang>
- Output:
<lang applescript>{1, 2, 3, 5, 4, 7, 9, 8, 11, 13, 6, 17, 19, 10, 21, 23, 16, 15, 29, 14, 25, 27, 22, 31, 35, 12, 37, 41, 18, 43, 47, 20, 33, 49, 26, 45}</lang>
Factor
<lang factor>USING: combinators.short-circuit.smart formatting grouping io kernel make math prettyprint sequences sets ;
- coprime? ( m n -- ? ) simple-gcd 1 = ;
- coprime-both? ( m n o -- ? ) '[ _ coprime? ] both? ;
- triplet? ( hs m n o -- ? )
{ [ coprime-both? nip ] [ 2nip swap in? not ] } && ;
- next ( hs m n -- hs' m' n' )
0 [ 4dup triplet? ] [ 1 + ] until nipd pick [ adjoin ] keepd ;
- (triplets-upto) ( n -- )
[ HS{ 1 2 } clone 1 , 1 2 ] dip '[ 2dup [ _ < ] both? ] [ dup , next ] while 3drop ;
- triplets-upto ( n -- seq ) [ (triplets-upto) ] { } make ;
"Coprime triplets under 50:" print 50 triplets-upto [ 9 group simple-table. nl ] [ length "Found %d terms.\n" printf ] bi</lang>
- Output:
Coprime triplets under 50: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45 Found 36 terms.
FreeBASIC
<lang freebasic>function gcd( a as uinteger, b as uinteger ) as uinteger
if b = 0 then return a return gcd( b, a mod b )
end function
function num_in_array( array() as integer, num as integer ) as boolean
for i as uinteger = 1 to ubound(array) if array(i) = num then return true next i return false
end function
redim as integer trips(1 to 2) trips(1) = 1 : trips(2) = 2 dim as integer last
do
last = ubound(trips) for q as integer = 1 to 49 if not num_in_array( trips(), q ) _ andalso gcd(q, trips(last)) = 1 _ andalso gcd(q, trips(last-1)) = 1 then redim preserve as integer trips( 1 to last+1 ) trips(last+1) = q continue do end if next q exit do
loop
print using "Found ## terms:"; ubound(trips)
for i as integer = 1 to last
print trips(i);" ";
next i : print</lang>
- Output:
Found 36 terms: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
Haskell
<lang haskell>import Data.List (find, transpose, unfoldr) import Data.List.Split (chunksOf) import qualified Data.Set as S
COPRIME TRIPLES --------------------
coprimeTriples :: Integral a => [a] coprimeTriples =
[1, 2] <> unfoldr go (S.fromList [1, 2], (1, 2)) where go (seen, (a, b)) = Just (c, (S.insert c seen, (b, c))) where Just c = find ( ((&&) . flip S.notMember seen) <*> ((&&) . coprime a <*> coprime b) ) [3 ..]
coprime :: Integral a => a -> a -> Bool coprime a b = 1 == gcd a b
TEST -------------------------
main :: IO () main =
let xs = takeWhile (< 50) coprimeTriples in putStrLn (show (length xs) <> " terms below 50:\n") >> putStrLn ( spacedTable justifyRight (chunksOf 10 (show <$> xs)) )
FORMAT ------------------------
spacedTable ::
(Int -> Char -> String -> String) -> String -> String
spacedTable aligned rows =
unlines $ unwords . zipWith (`aligned` ' ') (maximum . fmap length <$> transpose rows) <$> rows
justifyRight :: Int -> Char -> String -> String justifyRight n c = (drop . length) <*> (replicate n c <>)</lang>
- Output:
36 terms below 50: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
Julia
<lang julia>function coprime_triplets(less_than = 50)
cpt = [1, 2] while true m = 1 while m in cpt || gcd(m, cpt[end]) != 1 || gcd(m, cpt[end - 1]) != 1 m += 1 end m >= less_than && return cpt push!(cpt, m) end
end
trps = coprime_triplets() println("Found $(length(trps)) coprime triplets less than 50:") foreach(p -> print(rpad(p[2], 3), p[1] %10 == 0 ? "\n" : ""), enumerate(trps))
</lang>
- Output:
Found 36 coprime triplets less than 50: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
Phix
function coprime_triplets(integer less_than=50) sequence cpt = {1,2} while true do integer m = 1 while find(m,cpt) or gcd(m,cpt[$])!=1 or gcd(m,cpt[$-1])!=1 do m += 1 end while if m>=less_than then exit end if cpt &= m end while return cpt end function sequence res = apply(true,sprintf,{{"%2d"},coprime_triplets()}) printf(1,"Found %d coprime triplets:\n%s\n",{length(res),join_by(res,1,10," ")})
- Output:
Found 36 coprime triplets: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
Raku
<lang perl6>my @coprime-triplets = 1, 2, {
state %seen = 1, True, 2, True; state $min = 3; my $g = $^a * $^b; my $n = ($min .. *).first: { !%seen{$_} && ($_ gcd $g == 1) } %seen{$n} = True; if %seen.elems %% 100 { $min = ($min .. *).first: { !%seen{$_} } } $n
} … *;
put "Coprime triplets before first > 50:\n", @coprime-triplets[^(@coprime-triplets.first: * > 50, :k)].batch(10)».fmt("%4d").join: "\n";
put "\nOr maybe, minimum Coprime triplets that encompass 1 through 50:\n", @coprime-triplets[0..(@coprime-triplets.first: * == 42, :k)].batch(10)».fmt("%4d").join: "\n";
put "\nAnd for the heck of it: 1001st through 1050th Coprime triplet:\n", @coprime-triplets[1000..1049].batch(10)».fmt("%4d").join: "\n";</lang>
- Output:
Coprime triplets before first > 50: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45 Or maybe, minimum Coprime triplets that encompass 1 through 50: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45 53 28 39 55 32 51 59 38 61 63 34 65 57 44 67 69 40 71 73 24 77 79 30 83 89 36 85 91 46 75 97 52 81 95 56 87 101 50 93 103 58 99 107 62 105 109 64 111 113 68 115 117 74 119 121 48 125 127 42 And for the heck of it: 1001st through 1050th Coprime triplet: 682 1293 1361 680 1287 1363 686 1299 1367 688 1305 1369 692 1311 1373 694 1317 1375 698 1323 1381 704 1329 1379 706 1335 1387 716 1341 1385 712 1347 1391 700 1353 1399 710 1359 1393 718 1371 1397 722 1365 1403 724 1377 1405 728 1383
REXX
<lang rexx>/*REXX program finds and display coprime triplets below a specified limit (limit=50).*/ parse arg n cols . /*obtain optional arguments from the CL*/ if n== | n=="," then n= 50 /*Not specified? Then use the default.*/ if cols== | cols=="," then cols= 10 /* " " " " " " */ w= max(3, length( commas(n) ) ) /*width of a number in any column. */
@copt= ' coprime triplets where N < ' commas(n)
if cols>0 then say ' index │'center(@copt, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(W+1), '─') !.= 0; @.= !.; idx= 1; $= /*initialize some variables. */
do #=1 do j=1; if @.j then iterate /*J in list of coprime triplets? Skip.*/ if #<3 then leave /*First two entries not defined? Use it*/ a= # - 1; b= # - 2 /*get the last two indices of sequence.*/ if gcd(j, !.a)\==1 then iterate /*J not coprime with last number?*/ if gcd(j, !.b)\==1 then iterate /*" " " " penultimate " */ leave /*OK, we've found a new coprime triplet*/ end /*j*/ if j>=n then leave /*Have we exceeded the limit? Then quit*/ @.j= 1; !.#= j /*flag a coprime triplet (two methods).*/ if cols==0 then iterate /*Not showing the numbers? Keep looking*/ $= $ right( commas(j), w) /*append coprime triplet to output list*/ if #//cols\==0 then iterate /*Is output line full? No, keep looking*/ say center(idx, 7)'│' substr($, 2); $= /*show output line of coprime triplets.*/ idx= idx + cols /*bump the index for the output line. */ end /*forever*/
if $\== then say center(idx, 7)'│' substr($, 2) /*show any residual output numbers*/ if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') say say 'Found ' commas(#-1) @copt exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? gcd: procedure; parse arg x,y; do until _==0; _= x//y; x= y; y= _; end; return x</lang>
- output when using the default inputs:
index │ coprime triplets where N < 50 ───────┼───────────────────────────────────────── 1 │ 1 2 3 5 4 7 9 8 11 13 11 │ 6 17 19 10 21 23 16 15 29 14 21 │ 25 27 22 31 35 12 37 41 18 43 31 │ 47 20 33 49 26 45 ───────┴───────────────────────────────────────── Found 36 coprime triplets where N < 50
Ring
<lang ring> see "working..." + nl row = 2 numbers = 1:50 first = 1 second = 2 see "Coprime triplets are:" + nl see "" + first + " " + second + " "
for n = 3 to len(numbers) flag1 = 1 flag2 = 1 if first < numbers[n] min = first else min = numbers[n] ok for m = 2 to min if first%m = 0 and numbers[n]%m = 0 flag1 = 0 exit ok next if second < numbers[n] min = second else min = numbers[n] ok for m = 2 to min if second%m = 0 and numbers[n]%m = 0 flag2 = 0 exit ok next if flag1 = 1 and flag2 = 1 see "" + numbers[n] + " " first = second second = numbers[n] del(numbers,n) row = row+1 if row%10 = 0 see nl ok n = 2 ok next
see nl + "Found " + row + " coprime triplets" + nl see "done..." + nl
</lang>
- Output:
working... Coprime triplets are: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45 Found 36 coprime triplets done...
Wren
<lang ecmascript>import "/math" for Int import "/seq" for Lst import "/fmt" for Fmt
var limit = 50 var cpt = [1, 2]
while (true) {
var m = 1 while (cpt.contains(m) || Int.gcd(m, cpt[-1]) != 1 || Int.gcd(m, cpt[-2]) != 1) { m = m + 1 } if (m >= limit) break cpt.add(m)
} System.print("Coprime triplets under %(limit):") for (chunk in Lst.chunks(cpt, 10)) Fmt.print("$2d", chunk) System.print("\nFound %(cpt.count) such numbers.")</lang>
- Output:
Coprime triplets under 50: 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45 Found 36 such numbers.