N-smooth numbers: Difference between revisions
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'''n-smooth''' numbers are positive integers which have no prime factors <big> > </big> '''n'''.
The '''n'''
<br>there are <u>no</u> '''9-smooth''' numbers.
Line 1,258:
end.
</syntaxhighlight>
=={{header|Elm}}==
As mentioned on [[https://rosettacode.org/wiki/Hamming_numbers#Elm|the Hamming numbers task page]], currently Elm has many restrictions that make it difficult to implement finding a sequence of these numbers; as N-smooth numbers are just a more general case of Hamming numbers which include the latter, the code from that page is just re-factored to cover the more general case as follows:
<syntaxhighlight lang="elm">module Main exposing ( main )
import Bitwise exposing (..)
import BigInt exposing ( BigInt )
import Task exposing ( Task, succeed, perform, andThen )
import Html exposing ( div, text, br )
import Browser exposing ( element )
import Time exposing ( now, posixToMillis )
-- an infinite non-empty non-memoizing Co-Inductive Stream (CIS)...
type CIS a = CIS a (() -> CIS a)
takeCIS2String : Int -> (a -> String) -> CIS a -> String
takeCIS2String n cnvf (CIS ohd otlf) =
let loop i (CIS hd tl) str =
if i < 1 then str
else loop (i - 1) (tl()) (str ++ ", " ++ cnvf hd)
in loop (n - 1) (otlf()) (cnvf ohd)
dropCIS : Int -> CIS a -> CIS a
dropCIS n (CIS _ tl as cis) =
if n < 1 then cis else dropCIS (n - 1) (tl())
-- Priority Queue definition...
type PriorityQ comparable v =
Mt
| Br comparable v (PriorityQ comparable v)
(PriorityQ comparable v)
emptyPQ : PriorityQ comparable v
emptyPQ = Mt
peekMinPQ : PriorityQ comparable v -> Maybe (comparable, v)
peekMinPQ pq = case pq of
(Br k v _ _) -> Just (k, v)
Mt -> Nothing
pushPQ : comparable -> v -> PriorityQ comparable v
-> PriorityQ comparable v
pushPQ wk wv pq =
case pq of
Mt -> Br wk wv Mt Mt
(Br vk vv pl pr) ->
if wk <= vk then Br wk wv (pushPQ vk vv pr) pl
else Br vk vv (pushPQ wk wv pr) pl
siftdown : comparable -> v -> PriorityQ comparable v
-> PriorityQ comparable v -> PriorityQ comparable v
siftdown wk wv pql pqr =
case pql of
Mt -> Br wk wv Mt Mt
(Br vkl vvl pll prl) ->
case pqr of
Mt -> if wk <= vkl then Br wk wv pql Mt
else Br vkl vvl (Br wk wv Mt Mt) Mt
(Br vkr vvr plr prr) ->
if wk <= vkl && wk <= vkr then Br wk wv pql pqr
else if vkl <= vkr then Br vkl vvl (siftdown wk wv pll prl) pqr
else Br vkr vvr pql (siftdown wk wv plr prr)
replaceMinPQ : comparable -> v -> PriorityQ comparable v
-> PriorityQ comparable v
replaceMinPQ wk wv pq = case pq of
Mt -> Mt
(Br _ _ pl pr) -> siftdown wk wv pl pr
primesTo : Int -> List Int
primesTo n =
if n < 3 then if n < 2 then [] else [2] else
let oddPrimesTo on =
let sqrtlmt = toFloat on |> sqrt |> truncate
obps = if sqrtlmt < 3 then [] else oddPrimesTo sqrtlmt
ns = List.range 0 ((on - 3) // 2) -- [ 3 .. 2 .. on ]
|> List.map ((+) 3 << (*) 2)
filtfnc fn = List.all (\ bp -> bp * bp > fn ||
modBy bp fn /= 0) obps
in List.filter filtfnc ns
in 2 :: oddPrimesTo n
smooths : Int -> CIS BigInt
smooths n =
let infcis v = CIS v <| \ _ -> infcis (BigInt.add v (BigInt.fromInt 1))
dflt = (0.0, BigInt.fromInt 1) in
if n < 2 then infcis (BigInt.fromInt 1) else
let prms = primesTo n |> List.reverse
|> List.map (\ p -> (logBase 2 (toFloat p), BigInt.fromInt p))
((lgfrstp, frstp) as frstpr) = List.head prms |> Maybe.withDefault dflt
rstps = List.tail prms |> Maybe.withDefault []
frstcis =
let nxt ((lg, v) as vpr) =
CIS vpr <| \ _ -> nxt (lg + lgfrstp, BigInt.mul v frstp)
in nxt frstpr
mkcis ((lg, p) as pr) cis =
let nxt pq (CIS ((lghd, hd) as hdpr) tlf as cs) =
let ((lgv, v) as vpr) = peekMinPQ pq |> Maybe.withDefault dflt in
if BigInt.lt v hd then CIS vpr <| \ _ ->
nxt (replaceMinPQ (lgv + lg) (BigInt.mul v p) pq) cs
else CIS hdpr <| \ _ ->
nxt (pushPQ (lghd + lg) (BigInt.mul hd p) pq) (tlf())
in CIS pr <| \ _ -> nxt (pushPQ (lg + lg) (BigInt.mul p p) emptyPQ) cis
rest() = List.foldl mkcis frstcis rstps
unpr (CIS (_, hd) tlf) = CIS hd <| \ _ -> unpr (tlf())
in CIS (BigInt.fromInt 1) <| \ _ -> unpr (rest())
timemillis : () -> Task Never Int -- a side effect function
timemillis() = now |> andThen (\ t -> succeed (posixToMillis t))
test : () -> Cmd Msg -- side effect function chain (includes "perform")...
test() =
timemillis()
|> andThen (\ strt ->
let test1 = primesTo 29 |> List.map ( \ p ->
[ "The first 25 " ++ String.fromInt p ++ "-smooths:"
, smooths p |> takeCIS2String 25 BigInt.toString
, "" ])
test2 = primesTo 29 |> List.drop 1 |> List.map ( \ p ->
[ "The first three from the 3,000th "
++ String.fromInt p ++ "-smooth numbers are:"
, smooths p |> dropCIS 2999
|> takeCIS2String 3 BigInt.toString
, "" ])
test3 = primesTo 521 |> List.filter ((<=) 503) |> List.map ( \ p ->
[ "The first 20 30,000th up "
++ String.fromInt p ++ "-smooth numbers are:"
, smooths p |> dropCIS 29999
|> takeCIS2String 20 BigInt.toString
, "" ])
in timemillis()
|> andThen (\ stop ->
succeed ([test1, test2, test3, [[ "This took "
++ String.fromInt (stop - strt)
++ " milliseconds."]]]
|> List.concat |> List.concat)))
|> perform Done
-- following code has to do with outputting to a web page using MUV/TEA...
type alias Model = List String
type Msg = Done Model
main : Program () Model Msg
main = -- starts with empty list of strings; views model of filled list...
element { init = \ _ -> ( [], test() )
, update = \ (Done mdl) _ -> ( mdl , Cmd.none )
, subscriptions = \ _ -> Sub.none
, view = \ mdl ->
div [] <| List.map (\ s ->
if s == "" then br [] []
else div [] <| List.singleton <| text s) mdl
}</syntaxhighlight>
{{out}}
<pre>The first 25 13-smooths:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28
The first 25 17-smooths:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27
The first 25 19-smooths:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26
The first 25 23-smooths:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
The first 25 29-smooths:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
The first three from the 3,000th 3-smooth numbers are:
91580367978306252441724649472, 92829823186414819915547541504, 94096325042746502515294076928
The first three from the 3,000th 5-smooth numbers are:
278942752080, 279936000000, 281250000000
The first three from the 3,000th 7-smooth numbers are:
50176000, 50331648, 50388480
The first three from the 3,000th 11-smooth numbers are:
2112880, 2116800, 2117016
The first three from the 3,000th 13-smooth numbers are:
390000, 390390, 390625
The first three from the 3,000th 17-smooth numbers are:
145800, 145860, 146016
The first three from the 3,000th 19-smooth numbers are:
74256, 74358, 74360
The first three from the 3,000th 23-smooth numbers are:
46552, 46575, 46585
The first three from the 3,000th 29-smooth numbers are:
33516, 33524, 33534
The first 20 30,000th up 503-smooth numbers are:
62913, 62914, 62916, 62918, 62920, 62923, 62926, 62928, 62930, 62933, 62935, 62937, 62944, 62946, 62951, 62952, 62953, 62957, 62959, 62964
The first 20 30,000th up 509-smooth numbers are:
62601, 62602, 62604, 62607, 62608, 62609, 62611, 62618, 62620, 62622, 62624, 62625, 62626, 62628, 62629, 62634, 62640, 62643, 62645, 62646
The first 20 30,000th up 521-smooth numbers are:
62287, 62288, 62291, 62292, 62300, 62304, 62307, 62308, 62310, 62315, 62320, 62321, 62322, 62325, 62328, 62329, 62330, 62331, 62335, 62336
This took 506 milliseconds.</pre>
=={{header|F_Sharp|F#}}==
The easy way to solve this is just to translate the Haskell contribution as from "Hamming Numbers without duplicates", along with a version of a trial division small primes determination since the required primes have such a small range, as follows:
<syntaxhighlight lang="fsharp">let primesTo n =
if n < 3 then (if n < 2 then Seq.empty else Seq.singleton 2) else
let rec oddPrimesTo on =
let sqrtlmt = double on |> sqrt |> truncate |> int
let obps = if sqrtlmt < 3 then Seq.empty else oddPrimesTo sqrtlmt
let ns = [ 3 .. 2 .. on ]
let filtfnc fn = Seq.forall (fun bp -> bp * bp > fn ||
fn % bp <> 0) obps
Seq.filter filtfnc ns
Seq.append (Seq.singleton 2) (oddPrimesTo n)
type LazyList<'a> = Cons of 'a * Lazy<LazyList<'a>>
// Doesn't need to be that efficient for the task...
#nowarn "40" // don't need to warn for recursive values
let smooths p =
if p < 2 then Seq.singleton (bigint 1) else
let smthprms = primesTo p |> Seq.rev |> Seq.map bigint
let frstp = Seq.head smthprms
let rstps = Seq.tail smthprms
let frstll =
let rec nxt n =
Cons(n, lazy nxt (n * frstp))
nxt frstp
let smult m lzylst =
let rec smlt (Cons(x, rxs)) =
Cons(m * x, lazy(smlt (rxs.Force())))
smlt lzylst
let rec merge (Cons(x, f) as xs) (Cons(y, g) as ys) =
if x < y then Cons(x, lazy(merge (f.Force()) ys))
else Cons(y, lazy(merge xs (g.Force())))
let u s n =
let rec r = merge s (smult n (Cons(1I, lazy r))) in r
Seq.unfold (fun (Cons(hd, rst)) -> Some (hd, rst.Value))
(Cons(1I, lazy(Seq.fold u frstll rstps)))
let strt = System.DateTime.Now.Ticks
primesTo 29 |> Seq.iter (fun p ->
printfn "First 25 %d-smooth:" p
smooths p |> Seq.take 25 |> Seq.toList |> printfn "%A\r\n")
primesTo 29 |> Seq.skip 1 |> Seq.iter (fun p ->
printfn "The first three from the 3,000th %d-smooth numbers are:" p
smooths p |> Seq.skip 2999 |> Seq.take 3 |> Seq.toList |> printfn "%A\r\n")
primesTo 521 |> Seq.skipWhile ((>) 503) |> Seq.iter (fun p ->
printfn "The first 20 30,000th up %d-smooth numbers are:" p
smooths p |> Seq.skip 29999 |> Seq.take 20 |> Seq.toList |> printfn "%A\r\n")
let stop = System.DateTime.Now.Ticks
printfn "This took %d milliseconds." ((stop - strt) / 10000L)</syntaxhighlight>
{{out}}
<pre>First 25 2-smooth:
[1; 2; 4; 8; 16; 32; 64; 128; 256; 512; 1024; 2048; 4096; 8192; 16384; 32768;
65536; 131072; 262144; 524288; 1048576; 2097152; 4194304; 8388608; 16777216]
First 25 3-smooth:
[1; 2; 3; 4; 6; 8; 9; 12; 16; 18; 24; 27; 32; 36; 48; 54; 64; 72; 81; 96; 108;
128; 144; 162; 192]
First 25 5-smooth:
[1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 15; 16; 18; 20; 24; 25; 27; 30; 32; 36; 40; 45;
48; 50; 54]
First 25 7-smooth:
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 15; 16; 18; 20; 21; 24; 25; 27; 28; 30;
32; 35; 36]
First 25 11-smooth:
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 14; 15; 16; 18; 20; 21; 22; 24; 25; 27;
28; 30; 32]
First 25 13-smooth:
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 18; 20; 21; 22; 24; 25;
26; 27; 28]
First 25 17-smooth:
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 20; 21; 22; 24;
25; 26; 27]
First 25 19-smooth:
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22;
24; 25; 26]
First 25 23-smooth:
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22;
23; 24; 25]
First 25 29-smooth:
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22;
23; 24; 25]
The first three from the 3,000th 3-smooth numbers are:
[91580367978306252441724649472; 92829823186414819915547541504;
94096325042746502515294076928]
The first three from the 3,000th 5-smooth numbers are:
[278942752080; 279936000000; 281250000000]
The first three from the 3,000th 7-smooth numbers are:
[50176000; 50331648; 50388480]
The first three from the 3,000th 11-smooth numbers are:
[2112880; 2116800; 2117016]
The first three from the 3,000th 13-smooth numbers are:
[390000; 390390; 390625]
The first three from the 3,000th 17-smooth numbers are:
[145800; 145860; 146016]
The first three from the 3,000th 19-smooth numbers are:
[74256; 74358; 74360]
The first three from the 3,000th 23-smooth numbers are:
[46552; 46575; 46585]
The first three from the 3,000th 29-smooth numbers are:
[33516; 33524; 33534]
The first 20 30,000th up 503-smooth numbers are:
[62913; 62914; 62916; 62918; 62920; 62923; 62926; 62928; 62930; 62933; 62935;
62937; 62944; 62946; 62951; 62952; 62953; 62957; 62959; 62964]
The first 20 30,000th up 509-smooth numbers are:
[62601; 62602; 62604; 62607; 62608; 62609; 62611; 62618; 62620; 62622; 62624;
62625; 62626; 62628; 62629; 62634; 62640; 62643; 62645; 62646]
The first 20 30,000th up 521-smooth numbers are:
[62287; 62288; 62291; 62292; 62300; 62304; 62307; 62308; 62310; 62315; 62320;
62321; 62322; 62325; 62328; 62329; 62330; 62331; 62335; 62336]
This took 544 milliseconds.</pre>
As run on an Intel i5-6500 (3.6 GHz boosted when single-threaded), this isn't particularly fast, slowed by DotNet's poor allocation/deallocation of small memory area performance as required here for the "LazyList" implementation (a new allocation for each element) as well as the time to process the deferred execution "thunks" required for memoization, and also because the "BigInt" implementation isn't likely as fast as the "native" implementation used by some languages such as Haskell (by default).
'''Faster Non-recursive Version'''
The following code is over twice as fast because it no longer requires a memoized "LazyList" but just the deferred-execution tails of a Co-Inductive Stream (CIS), although to be general it still uses these streams for each merged CIS of the accumulated intermediate result streams, meaning that it still uses many allocations/deallocations for each CIS element; as well, it avoids some of the slow F# "Seq" operations by directly manipulating the "CIS" streams:
<syntaxhighlight lang="fsharp">let primesTo n =
if n < 3 then (if n < 2 then Seq.empty else Seq.singleton 2) else
let rec oddPrimesTo on =
let sqrtlmt = double on |> sqrt |> truncate |> int
let obps = if sqrtlmt < 3 then Seq.empty else oddPrimesTo sqrtlmt
let ns = [ 3 .. 2 .. on ]
let filtfnc fn = Seq.forall (fun bp -> bp * bp > fn ||
fn % bp <> 0) obps
Seq.filter filtfnc ns
Seq.append (Seq.singleton 2) (oddPrimesTo n)
type CIS<'a> = CIS of 'a * (Unit -> CIS<'a>)
let rec skipCIS n (CIS(_, tlf) as cis) =
if n <= 0 then cis else skipCIS (n - 1) (tlf())
let stringCIS n (CIS(fhd, ftlf)) =
let rec addstr i (CIS(hd, tlf)) str =
if i <= 0 then str + " )"
else addstr (i - 1) (tlf()) (str + ", " + string hd)
addstr (n - 1) (ftlf()) ("( " + string fhd)
type Deque<'a> = Deque of int * int * int * 'a array
let makeDQ v =
let arr = Array.zeroCreate 1024 in arr.[0] <- v
Deque(1023, 0, 1, arr)
let growDQ (Deque(msk, hdi, tli, arr)) =
let sz = arr.Length
let nsz = if sz = 0 then 1024 else sz + sz
let narr = Array.zeroCreate nsz
let nhdi, ntli =
if hdi = 0 then Array.blit arr 0 narr 0 sz
hdi, sz
else let mv = hdi + sz // move top queue up...
Array.blit arr 0 narr 0 tli
Array.blit arr hdi narr mv (sz - hdi)
mv, tli
Deque(nsz - 1, nhdi, ntli, narr)
let pushDQ v (Deque(_, hdi, tli, _) as dq) =
let (Deque(nmsk, nhdi, ntli, narr)) = if tli <> hdi then dq
else growDQ dq
narr.[ntli] <- v
Deque(nmsk, nhdi, (ntli + 1) &&& nmsk, narr)
// Deque is never empty after the first push and always push before pull!
let inline peekDQ (Deque(_, hdi, _, arr)) = arr.[hdi]
let pullDQ (Deque(msk, hdi, tli, arr)) =
Deque(msk, (hdi + 1) &&& msk, tli, arr)
let smoothsNR p =
// if p < 2 then Seq.singleton (bigint 1) else
let smthprms = primesTo p |> Seq.rev |> Seq.map bigint
let frstp = Seq.head smthprms
let rstps = Seq.tail smthprms
let frstcis =
let rec nxt n =
CIS(n, fun () -> nxt (n * frstp)) in nxt frstp
let nxt dq =
Seq.initInfinite ((+) 1I << bigint)
let newcis cis p =
let rec nxt (CIS(hd, tlf) as cs) dq =
let nxtq = peekDQ dq
if hd < nxtq then CIS(hd, fun () -> nxt (tlf()) (pushDQ (hd * p) dq))
else CIS(nxtq, fun () -> nxt cs (pushDQ (nxtq * p) dq |> pullDQ))
CIS(p, fun () -> nxt cis (makeDQ (p * p)))
CIS(1I, fun () -> Seq.fold newcis frstcis rstps)
let strt = System.DateTime.Now.Ticks
primesTo 29 |> Seq.iter (fun p ->
printfn "First 25 %d-smooth:" p
smoothsNR p |> stringCIS 25 |> printfn "%s\r\n")
primesTo 29 |> Seq.skip 1 |> Seq.iter (fun p ->
printfn "The first three from the 3,000th %d-smooth numbers are:" p
smoothsNR p |> skipCIS 2999 |> stringCIS 3 |> printfn "%s\r\n")
primesTo 521 |> Seq.skipWhile ((>) 503) |> Seq.iter (fun p ->
printfn "The first 20 from the 30,000th up %d-smooth numbers are:" p
smoothsNR p |> skipCIS 29999 |> stringCIS 20 |> printfn "%s\r\n")
let stop = System.DateTime.Now.Ticks
printfn "This took %d milliseconds." ((stop - strt) / 10000L)</syntaxhighlight>
=={{header|Factor}}==
Line 2,538 ⟶ 2,975:
=={{header|Pascal}}==
==={{
<syntaxhighlight lang="pascal">program nSmoothNumbers(output);
Line 2,803 ⟶ 3,240:
23-smooth: 3000 3003 3024
29-smooth: 3000 3003 3016</pre>
==={{header|Free Pascal}}===
misunderstood limit 3000 as n-smooth number index. So 2-smooth (3000) = 2^n was out of reach.
<syntaxhighlight lang="pascal">program HammNumb;
{$IFDEF FPC} {$MODE DELPHI} {$OPTIMIZATION ON,ALL}{$ENDIF}
{$IFDEF WINDOWS}{$APPTYPE CONSOLE}{$ENDIF}
type
tHamNum = record
hampot : array[0..167] of Word;
hampotmax,
hamNum : NativeUint;
end;
const
primes : array[0..167] of word =
(2, 3, 5, 7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71
,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151
,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233
,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317
,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419
,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503
,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607
,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701
,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811
,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911
,919,929,937,941,947,953,967,971,977,983,991,997);
var
HNum:tHamNum;
procedure OutHamNum(const HNum:tHamNum);
var
i : NativeInt;
Begin
with Hnum do
Begin
write(hamNum:12,' : ');
For i := 0 to hampotmax-1 do
Begin
if hampot[i] >0 then
if hampot[i] = 1 then
write(primes[i],'*')
else
write(primes[i],'^',hampot[i],'*');
end;
if hampot[hampotmax] >0 then
begin
write(primes[hampotmax]);
if hampot[hampotmax] > 1 then
write('^',hampot[hampotmax]);
end;
end;
writeln;
end;
procedure NextHammNum(var HNum:tHamNum;maxP:NativeInt);
var
q,p,nr,n,pIdx,momPrime : NativeUInt;
begin
//special case prime = 2
IF maxP = 0 then
begin
IF HNum.hampot[0] <> 0 then
HNum.hamNum *= 2
else
HNum.hamNum := 1;
inc(HNum.hampot[0]);
EXIT;
end;
n := HNum.hamNum;
repeat
inc(n);
nr := n;
pIdx := 0;
repeat
momPrime := primes[pIdx];
q := nr div momPrime;
p := 0;
While q*momPrime=nr do
Begin
inc(p);
nr := q;
q := nr div momPrime;
end;
HNum.hampot[pIdx] := p;
inc(pIdx);
until (nr=1) OR (pIdx > maxp)
//found one, than finished
until nr = 1;
With HNum do
Begin
hamNum := n;
hamPotmax := pIdx-1;
end;
end;
procedure OutXafterYSmooth(X,Y,SmoothIdx: NativeUInt);
var
i: NativeUint;
begin
IF SmoothIdx> High(primes) then
EXIT;
fillChar(HNum,SizeOf(HNum),#0);
i := 0;
While HNum.HamNum < Y do
NextHammNum(HNum,SmoothIdx);
write('first ',X,' after ',Y,' ',primes[SmoothIdx]:3,'-smooth numbers : ');
IF x >10 then
writeln;
for i := 1 to X-1 do
begin
write(HNum.HamNum,' ');
NextHammNum(HNum,SmoothIdx);
end;
writeln(HNum.HamNum,' ');
end;
var
j: NativeUint;
Begin
j := 0;
while primes[j] <= 29 do
Begin
OutXafterYSmooth(25,1,j);
inc(j);
end;
writeln;
j := 1;
while primes[j] <= 29 do
Begin
OutXafterYSmooth(3,3000,j);
inc(j);
end;
writeln;
while primes[j] < 503 do
inc(j);
while primes[j] <= 521 do
Begin
OutXafterYSmooth(20,30000,j);
OutHamNum(Hnum);
inc(j);
end;
writeln;
End.</syntaxhighlight>
{{out}}
<pre>first 25 after 1 2-smooth numbers :
1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216
first 25 after 1 3-smooth numbers :
1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192
first 25 after 1 5-smooth numbers :
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54
first 25 after 1 7-smooth numbers :
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36
first 25 after 1 11-smooth numbers :
1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32
first 25 after 1 13-smooth numbers :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28
first 25 after 1 17-smooth numbers :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27
first 25 after 1 19-smooth numbers :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26
first 25 after 1 23-smooth numbers :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
first 25 after 1 29-smooth numbers :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
first 3 after 3000 3-smooth numbers : 3072 3456 3888
first 3 after 3000 5-smooth numbers : 3000 3072 3125
first 3 after 3000 7-smooth numbers : 3000 3024 3072
first 3 after 3000 11-smooth numbers : 3000 3024 3025
first 3 after 3000 13-smooth numbers : 3000 3003 3024
first 3 after 3000 17-smooth numbers : 3000 3003 3024
first 3 after 3000 19-smooth numbers : 3000 3003 3024
first 3 after 3000 23-smooth numbers : 3000 3003 3024
first 3 after 3000 29-smooth numbers : 3000 3003 3016
first 20 after 30000 503-smooth numbers :
30000 30003 30005 30008 30012 30014 30015 30016 30020 30024 30030 30033 30039 30044 30046 30048 30049 30051 30056 30057
30057 : 3*43*233
first 20 after 30000 509-smooth numbers :
30000 30003 30005 30008 30012 30014 30015 30016 30020 30024 30030 30031 30033 30039 30044 30046 30048 30049 30051 30056
30056 : 2^3*13*17^2
first 20 after 30000 521-smooth numbers :
30000 30003 30005 30008 30012 30014 30015 30016 30020 30024 30030 30031 30033 30039 30044 30046 30048 30049 30051 30056
30056 : 2^3*13*17^2</pre>
=={{header|Perl}}==
Line 3,818 ⟶ 4,445:
{{libheader|Wren-math}}
{{libheader|Wren-big}}
<syntaxhighlight lang="
import "./big" for BigInt, BigInts
// cache all primes up to 521
| |||