Sequence of non-squares: Difference between revisions
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{{task|Arithmetic operations}}
;Task:
Show that the following remarkable formula gives the [http://www.research.att.com/~njas/sequences/A000037 sequence] of non-square [[wp:Natural_number|natural numbers]]:
<big> n + floor(1/2 + sqrt(n)) </big>
* Print out the values for <big> n </big> in the range '''1''' to '''22'''
* Show that no squares occur for <big> n </big> less than one million
This is sequence [[oeis:A000037|A000037]] in the '''OEIS''' database.
<br><br>
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">F non_square(Int n)
R n + Int(floor(1/2 + sqrt(n)))
print_elements((1..22).map(non_square))
F is_square(n)
R fract(sqrt(n)) == 0
L(i) 1 .< 10 ^ 6
I is_square(non_square(i))
print(‘Square found ’i)
L.break
L.was_no_break
print(‘No squares found’)</syntaxhighlight>
{{out}}
<pre>
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
No squares found
</pre>
=={{header|ABC}}==
<syntaxhighlight lang="abc">HOW TO RETURN non.square n:
RETURN n + floor (1/2 + root n)
HOW TO REPORT square n:
REPORT n = (floor root n)**2
FOR n IN {1..22}: WRITE non.square n
WRITE /
IF NO n IN {1..1000000} HAS square non.square n:
WRITE "No squares occur for n < 1.000.000"</syntaxhighlight>
{{out}}
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
No squares occur for n < 1.000.000</pre>
=={{header|Ada}}==
<
with Ada.Text_IO; use Ada.Text_IO;
Line 30 ⟶ 75:
end if;
end loop;
end Sequence_Of_Non_Squares_Test;</
{{out}}
<pre>
Line 42 ⟶ 87:
{{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}}
{{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386}}
<
main: (
Line 60 ⟶ 105:
FI
OD
)</
{{out}}
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
=={{header|ALGOL W}}==
<syntaxhighlight lang="algolw">begin
% check values of the function: f(n) = n + floor(1/2 + sqrt(n)) %
% are not squares %
integer procedure f ( integer value n ) ;
begin
n + entier( 0.5 + sqrt( n ) )
end f ;
logical noSquares;
% first 22 values of f %
for n := 1 until 22 do writeon( i_w := 1, f( n ) );
% check f(n) does not produce a square for n in 1..1 000 000 %
noSquares := true;
for n := 1 until 1000000 do begin
integer fn, rn;
fn := f( n );
rn := round( sqrt( fn ) );
if ( rn * rn ) = fn then begin
write( "Found square at: ", n );
noSquares := false
end if_fn_is_a_square
end for_n ;
if noSquares then write( "f(n) did not produce a square in 1 .. 1 000 000" )
else write( "f(n) produced a square" )
end.</syntaxhighlight>
{{out}}
<pre>
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
f(n) did not produce a square in 1 .. 1 000 000
</pre>
=={{header|APL}}==
Generate the first 22 numbers:
<syntaxhighlight lang="apl"> NONSQUARE←{(⍳⍵)+⌊0.5+(⍳⍵)*0.5}
NONSQUARE 22
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27</syntaxhighlight>
Show there are no squares in the first million:
<syntaxhighlight lang="apl"> HOWMANYSQUARES←{+⌿⍵=(⌊⍵*0.5)*2}
HOWMANYSQUARES NONSQUARE 1000000
0</syntaxhighlight>
=={{header|AppleScript}}==
<syntaxhighlight lang="applescript">on task()
set values to {}
set squareCount to 0
repeat with n from 1 to (1000000 - 1)
set v to n + (0.5 + n ^ 0.5) div 1
if (n ≤ 22) then set end of values to v
set sqrt to v ^ 0.5
if (sqrt = sqrt as integer) then set squareCount to squareCount + 1
end repeat
return "Values (n = 1 to 22): " & join(values, ", ") & (linefeed & ¬
"Number of squares (n < 1000000): " & squareCount)
end task
on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
task() </syntaxhighlight>
{{output}}
<syntaxhighlight lang="applescript">"Values (n = 1 to 22): 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27
Number of squares (n < 1000000): 0"</syntaxhighlight>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">f: function [n]->
n + floor 0.5 + sqrt n
loop 1..22 'i ->
print [i "->" f i]
i: new 1, nonSquares: new []
while [i<1000000][ 'nonSquares ++ f i, inc 'i]
squares: map 1..1001 'x -> x ^ 2
if? empty? intersection squares nonSquares -> print "Didn't find any squares!"
else -> print "Ooops! Something went wrong!"</syntaxhighlight>
{{out}}
<pre>1 -> 2
2 -> 3
3 -> 5
4 -> 6
5 -> 7
6 -> 8
7 -> 10
8 -> 11
9 -> 12
10 -> 13
11 -> 14
12 -> 15
13 -> 17
14 -> 18
15 -> 19
16 -> 20
17 -> 21
18 -> 22
19 -> 23
20 -> 24
21 -> 26
22 -> 27
Didn't find any squares!</pre>
=={{header|AutoHotkey}}==
ahk forum: [http://www.autohotkey.com/forum/post-276683.html#276683 discussion]
<
t .= (A_Index + floor(0.5 + sqrt(A_Index))) " "
MsgBox %t%
Line 73 ⟶ 235:
Loop 1000000
x := A_Index + floor(0.5 + sqrt(A_Index)), s += x = round(sqrt(x))**2
Msgbox Number of bad squares = %s% ; 0</
=={{header|AWK}}==
<
1 2
2 3
Line 101 ⟶ 263:
$ awk 'func f(n){return(n+int(.5+sqrt(n)))}BEGIN{for(i=1;i<100000;i++){n=f(i);r=int(sqrt(n));if(r*r==n)print n"is square"}}'
$</
=={{header|BASIC}}==
{{works with|FreeBASIC}}
{{works with|RapidQ}}
<
DIM j AS Double
DIM found AS Integer
Line 130 ⟶ 292:
END IF
NEXT i
IF found=0 THEN PRINT "No squares found"</
=={{header|BASIC256}}==
<syntaxhighlight lang="freebasic"># Display first 22 values
print "The first 22 numbers generated by the sequence are : "
for i = 1 to 22
print nonSquare(i); " ";
next i
print
# Check for squares up to one million
found = false
for i = 1 to 1e6
j = sqrt(nonSquare(i))
if j = int(j) then
found = true
print i, " square numbers found"
exit for
end if
next i
if not found then print "No squares found"
end
function nonSquare (n)
return n + int(0.5 + sqrt(n))
end function</syntaxhighlight>
=={{header|BBC BASIC}}==
<
S% = N% + SQR(N%) + 0.5
PRINT S%
Line 144 ⟶ 332:
IF S%/R% = R% STOP
NEXT
PRINT "No squares occur for n < 1000000"</
{{out}}
<pre>
Line 178 ⟶ 366:
Since BC is an arbitrary precision calculator, there are no issues in sqrt (it is enough to increase the scale variable upto the desired ''precision''), nor there are limits (but time) to how many non-squares we can compute.
<
scale = 20
Line 223 ⟶ 411:
}
quit</
The functions int, round, floor, ceil are taken from [http://www.pixelbeat.org/scripts/bc here] (int is slightly modified) ([http://www.pixelbeat.org/scripts/ Here] he states the license is GPL).
=={{header|
<syntaxhighlight lang="bqn"> NonSquare ← +⟜(⌊0.5+√)
IsSquare ← =⟜⌊√
NonSquare 1+↕22
⟨ 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27 ⟩
+´ IsSquare NonSquare 1+↕1e6
0</syntaxhighlight>
=={{header|Burlesque}}==
<syntaxhighlight lang="burlesque">
1 22r@{?s0.5?+av?+}[m
</syntaxhighlight>
=={{header|C}}==
<
#include <stdio.h>
#include <assert.h>
Line 257 ⟶ 453:
}
return 0;
}</
=={{header|C sharp|C#}}==
<
using System.Diagnostics;
Line 284 ⟶ 480:
}
}
}</
=={{header|C++}}==
<
#include <algorithm>
#include <vector>
Line 320 ⟶ 516:
}
return 0 ;
}</
{{out}}
<pre>
Line 327 ⟶ 523:
</pre>
Alternatively, without using an external library
<syntaxhighlight lang="cpp">
#include <cmath>
#include <cstdint>
#include <iostream>
uint32_t non_square(const uint32_t& n) {
return n + static_cast<uint32_t>(0.5 + sqrt(n));
}
int main() {
std::cout << "The first 22 non-square numbers:" << std::endl;
for ( uint32_t i = 1; i <= 22; ++i ) {
std::cout << non_square(i) << " ";
}
std::cout << std::endl << std::endl;
uint32_t count = 0;
for ( uint32_t i = 1; i < 1'000'000; ++i ) {
double square_root = sqrt(non_square(i));
if ( square_root == floor(square_root) ) {
count++;
}
}
std::cout << "Number of squares less than 1'000'000 produced by the formula: " << count << std::endl;
}
</syntaxhighlight>
{{ out }}
<pre>The first 22 non-square numbers:
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
Number of squares less than 1'000'000 produced by the formula: 0</pre>
=={{header|Chipmunk Basic}}==
{{trans|BASIC256}}
{{works with|Chipmunk Basic|3.6.4}}
<syntaxhighlight lang="basic">10 rem Sequence of non-squares
20 cls
30 ' Display first 22 values
40 for i = 1 to 22
50 print nonsqr(i) " ";
60 next i
70 print
80 ' Check for squares up to one million
90 found = 0
100 for i = 1 to 1000000
110 j = sqr(nonsqr(i))
120 if j = int(j) then
130 found = 1
140 print "Found square: " i
150 exit for
160 endif
170 next i
180 if found = 0 then print "No squares occur for n < 1000000"
190 end
200 sub nonsqr(n)
210 nonsqr = n+int(0.5+sqr(n))
220 return</syntaxhighlight>
=={{header|Clojure}}==
<syntaxhighlight lang="clojure">;; provides floor and sqrt, but we use Java's sqrt as it's faster
;; (Clojure's is more exact)
(use 'clojure.contrib.math)
Line 341 ⟶ 595:
(doseq [n (range 1 23)] (printf "%s -> %s\n" n (nonsqr n)))
(defn verify [] (not-any? square? (map nonsqr (range 1 1000000))) )</
=={{header|CLU}}==
<syntaxhighlight lang="clu">non_square = proc (n: int) returns (int)
return(n + real$r2i(0.5 + real$i2r(n)**0.5))
end non_square
is_square = proc (n: int) returns (bool)
return(n = real$r2i(real$i2r(n)**0.5))
end is_square
start_up = proc()
po: stream := stream$primary_output()
for n: int in int$from_to(1, 22) do
stream$puts(po, int$unparse(non_square(n)) || " ")
end
stream$putl(po, "")
begin
for n: int in int$from_to(1, 1000000) do
if is_square(non_square(n)) then exit square(n) end
end
stream$putl(po, "No squares found up to 1000000.")
end
except when square(n: int):
stream$putl(po, "Found square " || int$unparse(non_square(n))
|| " at n = " || int$unparse(n))
end
end start_up </syntaxhighlight>
{{out}}
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
No squares found up to 1000000.</pre>
=={{header|COBOL}}==
<syntaxhighlight lang="cobol"> IDENTIFICATION DIVISION.
PROGRAM-ID. NONSQR.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 NEWTON.
03 SQR-INP PIC 9(7)V9(5).
03 SQUARE-ROOT PIC 9(7)V9(5).
03 FILLER REDEFINES SQUARE-ROOT.
05 FILLER PIC 9(7).
05 FILLER PIC 9(5).
88 SQUARE VALUE ZERO.
03 SQR-TEMP PIC 9(7)V9(5).
01 SEQUENCE-VARS.
03 N PIC 9(7).
03 SEQ PIC 9(7).
01 SMALL-FMT.
03 N-O PIC Z9.
03 FILLER PIC XX VALUE ": ".
03 SEQ-O PIC Z9.
PROCEDURE DIVISION.
BEGIN.
DISPLAY "Sequence of non-squares from 1 to 22:"
PERFORM SMALL-NUMS VARYING N FROM 1 BY 1
UNTIL N IS GREATER THAN 22.
DISPLAY SPACES.
DISPLAY "Checking items up to 1 million..."
PERFORM CHECK-NONSQUARE VARYING N FROM 1 BY 1
UNTIL SQUARE OR N IS GREATER THAN 1000000.
IF SQUARE, DISPLAY "Square found at N = " N,
ELSE, DISPLAY "No squares found up to 1 million.".
STOP RUN.
SMALL-NUMS.
PERFORM NONSQUARE.
MOVE N TO N-O.
MOVE SEQ TO SEQ-O.
DISPLAY SMALL-FMT.
CHECK-NONSQUARE.
PERFORM NONSQUARE.
MOVE SEQ TO SQR-INP.
PERFORM SQRT.
NONSQUARE.
MOVE N TO SQR-INP.
PERFORM SQRT.
ADD 0.5, SQUARE-ROOT GIVING SEQ.
ADD N TO SEQ.
SQRT.
MOVE SQR-INP TO SQUARE-ROOT.
COMPUTE SQR-TEMP =
(SQUARE-ROOT + SQR-INP / SQUARE-ROOT) / 2.
PERFORM SQRT-LOOP UNTIL SQUARE-ROOT IS EQUAL TO SQR-TEMP.
SQRT-LOOP.
MOVE SQR-TEMP TO SQUARE-ROOT.
COMPUTE SQR-TEMP =
(SQUARE-ROOT + SQR-INP / SQUARE-ROOT) / 2.</syntaxhighlight>
{{out}}
<pre> 1: 2
2: 3
3: 5
4: 6
5: 7
6: 8
7: 10
8: 11
9: 12
10: 13
11: 14
12: 15
13: 17
14: 18
15: 19
16: 20
17: 21
18: 22
19: 23
20: 24
21: 26
22: 27
Checking items up to 1 million...
No squares found up to 1 million.</pre>
=={{header|CoffeeScript}}==
<
non_square = (n) -> n + Math.floor(1/2 + Math.sqrt(n))
Line 364 ⟶ 740:
console.log "success"
</syntaxhighlight>
{{out}}
Line 377 ⟶ 753:
{{works with|CCL}}
<
(flet ((non-square (n)
"Compute the N-th number of the non-square sequence"
Line 392 ⟶ 768:
:when (squarep (non-square n))
:do (format t "Found a square: ~D -> ~D~%"
n (non-square n)))))</
=={{header|D}}==
<
int nonSquare(in int n) pure nothrow @safe @nogc {
Line 408 ⟶ 784:
assert(ns != (cast(int)real(ns).sqrt) ^^ 2);
}
}</
{{out}}
<pre>[2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27]</pre>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{libheader| System.Math}}
{{Trans|C sharp}}
Small variation of C#
<syntaxhighlight lang="delphi">
program Sequence_of_non_squares;
uses
System.SysUtils, System.Math;
function nonsqr(i: Integer): Integer;
begin
Result := Trunc(i + Floor(0.5 + Sqrt(i)));
end;
var
i: Integer;
j: Double;
begin
for i := 1 to 22 do
write(nonsqr(i), ' ');
Writeln;
for i := 1 to 999999 do
begin
j := Sqrt(nonsqr(i));
if (j = Floor(j)) then
Writeln(i, 'Is Square');
end;
end.</syntaxhighlight>
{{out}}
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
func nonSqu n .
return n + floor (0.5 + sqrt n)
.
for i = 1 to 22
print nonSqu i
.
for i = 1 to 1e6
j = sqrt nonSqu i
if j = floor j
found = 1
.
.
if found = 0
print "No squares found"
.
</syntaxhighlight>
=={{header|EchoLisp}}==
<
(lib 'sequences)
Line 423 ⟶ 854:
(filter square? (take A000037 1000000))
→ null
</syntaxhighlight>
=={{header|Eiffel}}==
<syntaxhighlight lang="eiffel">
class
APPLICATION
Line 471 ⟶ 902:
end
</syntaxhighlight>
{{out}}
<pre>
Line 506 ⟶ 937:
1001000
There are no squares for n equal to 1000000.
</pre>
=={{header|Elixir}}==
<syntaxhighlight lang="elixir">f = fn n -> n + trunc(0.5 + :math.sqrt(n)) end
IO.inspect for n <- 1..22, do: f.(n)
n = 1_000_000
non_squares = for i <- 1..n, do: f.(i)
m = :math.sqrt(f.(n)) |> Float.ceil |> trunc
squares = for i <- 1..m, do: i*i
case Enum.find_value(squares, fn i -> i in non_squares end) do
nil -> IO.puts "No squares found below #{n}"
val -> IO.puts "Error: number is a square: #{val}"
end</syntaxhighlight>
{{out}}
<pre>
[2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26,
27]
No squares found below 1000000
</pre>
=={{header|Erlang}}==
<
-module(non_squares).
-export([main/0]).
Line 518 ⟶ 970:
non_square(N) ->
N+trunc(1/2+ math:sqrt(N)).
</syntaxhighlight>
=={{header|Euphoria}}==
This is based on the [[BASIC]] and [[Go]] examples.
<
return n + floor( 0.5 + sqrt( n ) )
end function
Line 545 ⟶ 997:
if found = 0 then
puts( 1, "No squares found\n" )
end if</
=={{header|F_Sharp|F#}}==
<
let SequenceOfNonSquares =
Line 557 ⟶ 1,009:
|> Seq.map(fun f -> (f, nonsqr f))
|> Seq.filter(fun f -> IsSquare(snd f))
;;</
Executing the code gives:<
> SequenceOfNonSquares;;
val it : seq<int * int> = seq []</
=={{header|Factor}}==
<syntaxhighlight lang="factor">USING: kernel math math.functions math.ranges prettyprint
sequences ;
: non-sq ( n -- m ) dup sqrt 1/2 + floor + >integer ;
: print-first22 ( -- ) 22 [1,b] [ non-sq ] map . ;
: check-for-sq ( -- ) 1,000,000 [1,b)
[ non-sq sqrt dup floor = [ "Square found." throw ] when ]
each ;
print-first22 check-for-sq</syntaxhighlight>
{{out}}
<pre>
{ 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27 }
</pre>
=={{header|Fantom}}==
<
class Main
{
Line 587 ⟶ 1,057:
}
}
</syntaxhighlight>
=={{header|Forth}}==
<
: f>u f>d drop ;
Line 599 ⟶ 1,069:
: square? ( n -- ? ) u>f fsqrt fdup fround f- f0= ;
: test ( n -- ) 1 do i fn square? if cr i . ." fn was square" then loop ;
1000000 test \ ok</
=={{header|Fortran}}==
{{works with|Fortran|90 and later}}
<
IMPLICIT NONE
Line 622 ⟶ 1,092:
END DO
END PROGRAM NONSQUARES</
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">' FB 1.05.0 Win64
Function nonSquare (n As UInteger) As UInteger
Return CUInt(n + Int(0.5 + Sqr(n)))
End Function
Function isSquare (n As UInteger) As Boolean
Dim As UInteger r = CUInt(Sqr(n))
Return n = r * r
End Function
Print "The first 22 numbers generated by the sequence are :"
For i As Integer = 1 To 22
Print nonSquare(i); " ";
Next
Print : Print
' Test numbers generated for n less than a million to see if they're squares
For i As UInteger = 1 To 999999
If isSquare(nonSquare(i)) Then
Print "The number generated by the sequence for n ="; i; " is square!"
Goto finish
End If
Next
Print "None of the numbers generated by the sequence for n < 1000000 are square"
finish:
Print
Print "Press any key to quit"
Sleep</syntaxhighlight>
{{out}}
<pre>
The first 22 numbers generated by the sequence are :
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
None of the numbers generated by the sequence for n < 1000000 are square
</pre>
=={{header|GAP}}==
<syntaxhighlight lang="text"># Here we use generators : the given formula doesn't need one, but the alternate
# non-squares function is better done with a generator.
Line 669 ⟶ 1,182:
ForAll([1 .. 1000000], i -> a() = b());
# true</
=={{header|Go}}==
I assume it's obvious that the function monotonically increases, thus it's enough to just watch for the next possible square. If a square is found, the panic will cause an ugly stack trace.
<
import (
Line 709 ⟶ 1,222:
}
fmt.Println("No squares occur for n <", limit)
}</
{{out}}
<pre>
Line 751 ⟶ 1,264:
Solution:
<
Test Program:
<
(1..1000000).each { assert ((nonSquare(it)**0.5 as long)**2) != nonSquare(it) }</
{{out}}
Line 782 ⟶ 1,295:
=={{header|Haskell}}==
<
nonsqr n = n + round (sqrt (fromIntegral n))</
> map nonsqr [1..22]
Line 790 ⟶ 1,303:
> any (\j -> j == fromIntegral (floor j)) $ map (sqrt . fromIntegral . nonsqr) [1..1000000]
False
Or, in a point-free variation, defining a 'main' for the compiler (rather than interpreter)
<syntaxhighlight lang="haskell">import Control.Monad (join)
----------------------- NON SQUARES ----------------------
notSquare :: Int -> Bool
notSquare = (/=) <*> (join (*) . floor . root)
nonSqr :: Int -> Int
nonSqr = (+) <*> (round . root)
root :: Int -> Float
root = sqrt . fromIntegral
-------------------------- TESTS -------------------------
main :: IO ()
main =
mapM_
putStrLn
[ "First 22 members of the series:",
unwords $ show . nonSqr <$> [1 .. 22],
"",
"All first 10E6 members non square:",
(show . and) $
notSquare . nonSqr <$> [1 .. 1000000]
]</syntaxhighlight>
{{Out}}
<pre>First 22 members of the series:
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
All first 10E6 members non square:
True</pre>
=={{header|HicEst}}==
<
nonSqr = $ + FLOOR(0.5 + $^0.5)
Line 804 ⟶ 1,353:
ENDDO
WRITE(Name) squares_found
END</
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
squares_found=0; </pre>
=={{header|Icon}} and {{header|Unicon}}==
<
procedure main()
Line 823 ⟶ 1,372:
procedure nsq(n) # return non-squares
return n + floor(0.5 + sqrt(n))
end</
{{libheader|Icon Programming Library}}
[http://www.cs.arizona.edu/icon/library/src/procs/numbers.icn numbers provides floor]
=={{header|IDL}}==
<
f = n+floor(.5+sqrt(n)) ; Apply formula
print,f[0:21] ; Output first 22
print,where(sqrt(f) eq fix(sqrt(f))) ; Test for squares</
{{out}}
Line 843 ⟶ 1,392:
=={{header|J}}==
<
rf 1+i.22 NB. Results from 1 to 22
Line 849 ⟶ 1,398:
+/ (rf e. *:) 1+i.1e6 NB. Number of square RFs <= 1e6
0</
=={{header|Java}}==
<
public static int nonsqr(int n) {
return n + (int)Math.round(Math.sqrt(n));
Line 869 ⟶ 1,418:
}
}
}</
=={{header|JavaScript}}==
===ES5===
Iterative
<syntaxhighlight lang="javascript">var a = [];
for (var i = 1; i < 23; i++) a[i] = i + Math.floor(1/2 + Math.sqrt(i));
console.log(a);
Line 878 ⟶ 1,432:
for (i = 1; i < 1000000; i++) if (Number.isInteger(i + Math.floor(1/2 + Math.sqrt(i))) === false) {
console.log("The ",i,"th element of the sequence is a square");
}</
===ES6===
By functional composition
<syntaxhighlight lang="javascript">(() => {
'use strict';
// ------------------ OEIS A000037 -------------------
// nonSquare :: Int -> Int
const nonSquare = n =>
// Nth term in the OEIS A000037 series.
n + Math.floor(1 / 2 + Math.sqrt(n));
// isPerfectSquare :: Int -> Bool
const isPerfectSquare = n => {
const root = Math.sqrt(n);
return root === Math.floor(root);
};
// ---------------------- TEST -----------------------
const main = () =>
// First 22 terms, and test of first million.
[
Tuple('First 22 terms:')(
take(22)(
fmapGen(nonSquare)(
enumFrom(1)
)
)
),
Tuple(
'Any perfect squares in 1st 1E6 terms ?'
)(
Array.from({
length: 1E6
})
.map(nonSquare)
.some(isPerfectSquare)
)
]
.map(kv => `${fst(kv)} -> ${snd(kv)}`)
.join('\n\n');
// --------------------- GENERAL ---------------------
// Tuple (,) :: a -> b -> (a, b)
const Tuple = a =>
b => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});
// enumFrom :: Enum a => a -> [a]
function* enumFrom(x) {
// A non-finite succession of enumerable
// values, starting with the value x.
let v = x;
while (true) {
yield v;
v = 1 + v;
}
}
// fmapGen <$> :: (a -> b) -> Gen [a] -> Gen [b]
const fmapGen = f =>
function* (gen) {
let v = take(1)(gen);
while (0 < v.length) {
yield(f(v[0]));
v = take(1)(gen);
}
};
// fst :: (a, b) -> a
const fst = tpl =>
// First member of a pair.
tpl[0];
// snd :: (a, b) -> b
const snd = tpl =>
// Second member of a pair.
tpl[1];
// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = n =>
// The first n elements of a list,
// string of characters, or stream.
xs => 'GeneratorFunction' !== xs
.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));
return main()
})();</syntaxhighlight>
{{Out}}
<pre>First 22 terms: -> 2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27
Any perfect squares in 1st 1E6 terms ? -> false</pre>
=={{header|jq}}==
{{works with|jq|1.4}}
<
def is_square: sqrt | . == floor;
Line 889 ⟶ 1,554:
(range(1;23) | A000037),
"Check for squares for n up to 1e6:",
(range(1;1e6+1) | A000037 | select( is_square ))</
{{out}}
<
For n up to and including 22:
2
Line 916 ⟶ 1,581:
27
Check for squares for n up to 1e6:
$</
=={{header|Julia}}==
<syntaxhighlight lang="julia">nonsquare(n::Real) = n + floor(typeof(n), 0.5 + sqrt(n))
@show nonsquare.(1:1_000_000) ∩ collect(1:1000) .^ 2</syntaxhighlight>
{{out}}
<pre>nonsquare.(1:1000000) ∩ collect(1:1000) .^ 2 = Int64[]</pre>
So the set of squares of integers between 1 and 1000 and the first 1000000 terms of the given sequence is empty. Note that the given sequence is increasing and that its last term has a square root slightly less than 1000.5.
=={{header|K}}==
<syntaxhighlight lang="k"> nonsquare:{x+_.5+%x}
nonsquare[1_!23]</syntaxhighlight>
{{out}}
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27</pre>
<syntaxhighlight lang="k"> issquare:{(%x)=_%x}
+/issquare[nonsquare[1_!1000001]] / Number of squares in first million results</syntaxhighlight>
{{out}}
<pre>0</pre>
=={{header|Kotlin}}==
<syntaxhighlight lang="scala">// version 1.1
fun f(n: Int) = n + Math.floor(0.5 + Math.sqrt(n.toDouble())).toInt()
fun main(args: Array<String>) {
println(" n f")
val squares = mutableListOf<Int>()
for (n in 1 until 1000000) {
val v1 = f(n)
val v2 = Math.sqrt(v1.toDouble()).toInt()
if (v1 == v2 * v2) squares.add(n)
if (n < 23) println("${"%2d".format(n)} : $v1")
}
println()
if (squares.size == 0) println("There are no squares for n less than one million")
else println("Squares are generated for the following values of n: $squares")
}</syntaxhighlight>
{{out}}
<pre>
n f
1 : 2
2 : 3
3 : 5
4 : 6
5 : 7
6 : 8
7 : 10
8 : 11
9 : 12
10 : 13
11 : 14
12 : 15
13 : 17
14 : 18
15 : 19
16 : 20
17 : 21
18 : 22
19 : 23
20 : 24
21 : 26
22 : 27
There are no squares for n less than one million
</pre>
=={{header|Lambdatalk}}==
<syntaxhighlight lang="scheme">
{def nosquare {lambda {:n} {+ :n {floor {+ 0.5 {sqrt :n}}}}}}
-> nosquare
{def issquare {lambda {:n} {= {sqrt :n} {round {sqrt :n}}}}}
-> issquare
{S.map nosquare {S.serie 1 22}}
-> 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
{S.replace false by in
{S.map issquare _
{S.map nosquare
{S.serie 1 1000000}}}}
-> true
</syntaxhighlight>
=={{header|Liberty BASIC}}==
<syntaxhighlight lang="lb">
for i = 1 to 22
print nonsqr( i); " ";
Line 950 ⟶ 1,689:
nonsqr = n +int( 0.5 +n^0.5)
end function
</syntaxhighlight>
<pre>
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
Line 957 ⟶ 1,696:
=={{header|Logo}}==
<
=={{header|Lua}}==
<syntaxhighlight lang="lua">function nonSquare (n)
return n + math.floor(1/2 + math.sqrt(n))
end
for n = 1, 22 do
io.write(nonSquare(n) .. " ")
end
print()
local sr
for n = 1, 10^6 do
sr = math.sqrt(nonSquare(n))
if sr == math.floor(sr) then
print("Result for n = " .. n .. " is square!")
os.exit()
end
end
print("No squares found")</syntaxhighlight>
{{out}}
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
No squares found</pre>
=={{header|MAD}}==
<syntaxhighlight lang="mad"> NORMAL MODE IS INTEGER
BOOLEAN FOUND
FOUND = 0B
R SEQUENCE OF NON-SQUARES FORMULA
R FLOOR IS AUTOMATIC DUE TO INTEGER MATH
INTERNAL FUNCTION NONSQR.(N) = N+(.5+SQRT.(N))
R PRINT VALUES FOR 1..N..22
THROUGH SHOW, FOR N=1, 1, N.G.22
SHOW PRINT FORMAT OUTFMT,N,NONSQR.(N)
VECTOR VALUES OUTFMT = $I2,2H: ,I2*$
R CHECK FOR NO SQUARES UP TO ONE MILLION
THROUGH CHECK, FOR N=1, 1, N.GE.1000000
X=NONSQR.(N)
Y=SQRT.(X)
WHENEVER Y*Y.E.X
PRINT FORMAT FINDSQ,N,X
FOUND = 1B
CHECK END OF CONDITIONAL
WHENEVER .NOT. FOUND, PRINT FORMAT NOSQ
VECTOR VALUES FINDSQ = $5HELEM ,I5,2H, ,I5,11H, IS SQUARE*$
VECTOR VALUES NOSQ = $16HNO SQUARES FOUND*$
END OF PROGRAM</syntaxhighlight>
{{out}}
<pre> 1: 2
2: 3
3: 5
4: 6
5: 7
6: 8
7: 10
8: 11
9: 12
10: 13
11: 14
12: 15
13: 17
14: 18
15: 19
16: 20
17: 21
18: 22
19: 23
20: 24
21: 26
22: 27
NO SQUARES FOUND</pre>
=={{header|Maple}}==
<syntaxhighlight lang="maple">
with(NumberTheory):
nonSquareSequence := proc(n::integer)
return n + floor(1 / 2 + sqrt(n));
end proc:
seq(nonSquareSequence(i), i = 1..22);
for number from 1 to 10^6 while not issqr(nonSquareSequence(number)) do end;
number;
</syntaxhighlight>
{{out}}<pre>
2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26,
27
1000001
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
nonsq@Range[22]
If[! Or @@ (IntegerQ /@ Sqrt /@ nonsq@Range[10^6]),
Print["No squares for n <= ", 10^6]
]</
{{out}}
<pre>{2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27}
Line 973 ⟶ 1,810:
=={{header|MATLAB}}==
<
for n = (1:i)
Line 991 ⟶ 1,828:
fprintf('\nNo square numbers were generated for n <= %d\n',i);
end</
Solution:
<
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
No square numbers were generated for n <= 1000000</
No loops
<syntaxhighlight lang="matlab">
sum(ismember((1:1:sqrt(1e6-1)).^2,(1:1e6-1) + floor(1/2 + sqrt((1:1e6-1)))))
</syntaxhighlight>
=={{header|Maxima}}==
<
makelist(nonsquare(n), n, 1, 20);
[2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24]
Line 1,007 ⟶ 1,849:
u: makelist(i, i, 1, m)$
is(sublist(u, not_square) = sublist(map(nonsquare, u), lambda([x], x <= m)));
true</
=={{header|min}}==
{{works with|min|0.19.3}}
<syntaxhighlight lang="min">(dup sqrt 0.5 + int +) :non-sq
(sqrt dup floor - 0 ==) :sq?
(:n =q 1 'dup q concat 'succ concat n times pop) :upto
(non-sq print! " " print!) 22 upto newline
"Squares for n below one million:" puts!
(non-sq 'sq? 'puts when pop) 999999 upto</syntaxhighlight>
{{out}}
<pre>
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
Squares for n below one million:
</pre>
=={{header|Miranda}}==
<syntaxhighlight lang="miranda">main :: [sys_message]
main = [Stdout (lay [first22, hassquare])]
first22 :: [char]
first22 = show (take 22 nonsqrseq)
hassquare :: [char]
hassquare = "Square found", if or [issquare n | n<-take 1000000 nonsqrseq]
= "No square found", otherwise
issquare :: num->bool
issquare n = n == (entier (sqrt n))^2
nonsqrseq :: [num]
nonsqrseq = map nonsqr [1..]
nonsqr :: num->num
nonsqr n = n + entier (0.5 + sqrt n)</syntaxhighlight>
{{out}}
<pre>[2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27]
No square found</pre>
=={{header|МК-61/52}}==
<syntaxhighlight lang="text">1 П4 ИП4 0 , 5 ИП4 КвКор + [x]
+ С/П КИП4 БП 02</
=={{header|MMIX}}==
<
GREG @
buf OCTA 0,0
Line 1,100 ⟶ 1,980:
LDA $255,NL
TRAP 0,Fputs,StdOut
TRAP 0,Halt,0 % }</
{{out}}
<pre>~/MIX/MMIX/Rosetta> mmix SoNS
Line 1,107 ⟶ 1,987:
=={{header|Modula-3}}==
<
IMPORT IO, Fmt, Math;
Line 1,129 ⟶ 2,009:
END;
END;
END NonSquare.</
{{out}}
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27</pre>
=={{header|Nim}}==
<
result =
for i in 1..n:
result
func issqr(n: int): bool =
sqrt(float(n)).splitDecimal().floatpart < 1e-7
echo "Sequence for n = 22:"
echo nosqr(22).join(" ")
assert not issqr(i)
echo "\nNo squares were found for n less than 1_000_000."</syntaxhighlight>
{{out}}
<pre>Sequence for n = 22:
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
No squares were found for n less than 1_000_000.</pre>
=={{header|OCaml}}==
<
val nonsqr : int -> int = <fun>
# (* first 22 values (as a list) has no squares: *)
Line 1,168 ⟶ 2,052:
assert (j <> floor j)
done;;
- : unit = ()</
=={{header|Oforth}}==
<
1000000 seq map(#[ dup sqrt 0.5 + floor + ]) conform(#[ sqrt dup floor <>]) println</
{{out}}
Line 1,181 ⟶ 2,065:
1
</pre>
=={{header|Ol}}==
<syntaxhighlight lang="scheme">
(import (lib math))
(print
; sequence for 1 .. 22
(map (lambda (n)
(+ n (floor (+ 1/2 (exact (sqrt n))))))
(iota 22 1)))
; ==> (2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27)
(print
; filter out non squares
(filter
(lambda (x)
(let ((s (floor (exact (sqrt x)))))
(= (* s s) x)))
(map (lambda (n)
(+ n (floor (+ 1/2 (exact (sqrt n))))))
(iota 1000000 1))))
; ==> ()
</syntaxhighlight>
=={{header|Oz}}==
<
fun {NonSqr N}
N + {Float.toInt {Floor 0.5 + {Sqrt {Int.toFloat N}}}}
Line 1,199 ⟶ 2,107:
in
{Show {List.take Ns 22}}
{Show {Some Ns IsSquare}}</
=={{header|PARI/GP}}==
<
=={{header|Pascal}}==
{{libheader|Math}}
<
uses
Line 1,229 ⟶ 2,137:
writeln('square found for n = ', n);
end;
end.</
{{out}}
<pre>:> ./SequenceOfNonSquares
Line 1,237 ⟶ 2,145:
a little speedup in testing upto 1 billion.
5 secs instead of 21 secs using fpc2.6.4
<
//sequence of non-squares
//n = i + floor(1/2 + sqrt(i))
Line 1,286 ⟶ 2,194:
First22;
Test(1000*1000*1000);
end.</
=={{header|Perl}}==
<
print join(' ', map nonsqr($_), 1..22), "\n";
foreach my $i (1..1_000_000) {
my $
}</
{{out}}
<pre>2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27</pre>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">22</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">nxt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">snxt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nxt</span><span style="color: #0000FF;">*</span><span style="color: #000000;">nxt</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1000000</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">></span><span style="color: #000000;">snxt</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- printf(1,"%d didn't occur\n",snxt)</span>
<span style="color: #000000;">nxt</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">snxt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nxt</span><span style="color: #0000FF;">*</span><span style="color: #000000;">nxt</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">snxt</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"error!!\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"none found "</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?{</span><span style="color: #000000;">nxt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">snxt</span><span style="color: #0000FF;">}</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 1,333 ⟶ 2,238:
none found {1001,1002001}
</pre>
=={{header|Phixmonti}}==
<syntaxhighlight lang="Phixmonti">include ..\Utilitys.pmt
def non-sq dup sqrt 0.5 + int + enddef
22 for dup print ", " print non-sq ? endfor
1000000 for
non-sq sqrt dup int == if "Square found." ? exitfor endif
endfor</syntaxhighlight>
{{out}}
<pre>1, 2
2, 3
3, 5
4, 6
5, 7
6, 8
7, 10
8, 11
9, 12
10, 13
11, 14
12, 15
13, 17
14, 18
15, 19
16, 20
17, 21
18, 22
19, 23
20, 24
21, 26
22, 27
=== Press any key to exit ===</pre>
=={{header|PHP}}==
<
//First Task
for($i=1;$i<=22;$i++){
Line 1,355 ⟶ 2,296:
echo("Up to 1000000, found no square number in the sequence!");
}
?></
{{Out}}
<pre>>php nsqrt.php
Line 1,383 ⟶ 2,324:
Up to 1000000, found no square number in the sequence!
></pre>
=={{header|Picat}}==
<syntaxhighlight lang="picat">go =>
println([f(I) : I in 1..22]),
nl,
check(1_000_000),
nl.
% The formula
f(N) = N + floor(1/2 + sqrt(N)).
check(Limit) =>
Squares = new_map([I*I=1:I in 1..sqrt(Limit)]),
Check = [[I,T] : I in 1..Limit-1, T=f(I), Squares.has_key(T)],
println(check=Check.len).</syntaxhighlight>
{{out}}
<pre>[2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27]
check = 0</pre>
=={{header|PicoLisp}}==
<
(+ N (sqrt N T)) ) # 'sqrt' rounds when called with 'T'
Line 1,394 ⟶ 2,356:
(let (N (sqfun I) R (sqrt N))
(when (= N (* R R))
(prinl N " is square") ) ) )</
{{out}}
<pre>1 2
Line 1,420 ⟶ 2,382:
=={{header|PL/I}}==
<syntaxhighlight lang="pl/i">
put skip edit ((n, n + floor(sqrt(n) + 0.5) do n = 1 to n))
(skip, 2 f(5));
</syntaxhighlight>
Results:
<syntaxhighlight lang="text">
1 2
2 3
Line 1,449 ⟶ 2,411:
20 24
21 26
</syntaxhighlight>
Test 1,000,000 values:
<syntaxhighlight lang="text">
test: proc options (main);
declare n fixed (15);
Line 1,471 ⟶ 2,433:
end test;
</syntaxhighlight>
=={{header|PostScript}}==
<syntaxhighlight lang="text">/nonsquare { dup sqrt .5 add floor add } def
/issquare { dup sqrt floor dup mul eq } def
Line 1,484 ⟶ 2,446:
} if pop
} for
</syntaxhighlight>
{{out}} (lack of error message shows none below 1000 produced a square)
<pre>
Line 1,513 ⟶ 2,475:
=={{header|PowerShell}}==
Implemented as a filter here, which can be used directly on the pipeline.
<
return $_ + [Math]::Floor(1/2 + [Math]::Sqrt($_))
}</
Printing out the first 22 values is straightforward, then:
<syntaxhighlight lang
If there were any squares for ''n'' up to one million, they would be printed with the following, but there is no output:
<
| Get-NonSquare `
| Where-Object {
$r = [Math]::Sqrt($_)
[Math]::Truncate($r) -eq $r
}</
=={{header|PureBasic}}==
<
For a = 1 To 22
; Integer, so no floor needed
Line 1,553 ⟶ 2,515:
EndIf
; Wait for enter
Input()</
=={{header|Python}}==
<
>>> def non_square(n):
>>> # first 22 values has no squares:
>>> print(*map(non_square, range(1, 23)))
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
>>> # The following check shows no squares up to one million:
>>>
>>> non_squares = map(non_square, range(1, 10 ** 6))
>>> next(filter(is_square, non_squares))
StopIteration Traceback (most recent call last)
<ipython-input-45-f32645fc1c0a> in <module>()
1 non_squares = map(non_square, range(1, 10 ** 6))
----> 2 next(filter(is_square, non_squares))
StopIteration: </syntaxhighlight>
Or, defining OEIS A000037 as a non-finite series:
{{Works with|Python|3.7}}
<syntaxhighlight lang="python">'''Sequence of non-squares'''
from itertools import count, islice
from math import floor, sqrt
# A000037 :: [Int]
def A000037():
'''A non-finite series of integers.'''
return map(nonSquare, count(1))
# nonSquare :: Int -> Int
def nonSquare(n):
'''Nth term in the OEIS A000037 series.'''
return n + floor(1 / 2 + sqrt(n))
# --------------------------TEST---------------------------
# main :: IO ()
def main():
'''OEIS A000037'''
def first22():
'''First 22 terms'''
return take(22)(A000037())
def squareInFirstMillion():
'''True if any of the first 10^6 terms are perfect squares'''
return any(map(
isPerfectSquare,
take(10 ** 6)(A000037())
))
print(
fTable(main.__doc__)(
lambda f: '\n' + f.__doc__
)(lambda x: ' ' + showList(x))(
lambda f: f()
)([first22, squareInFirstMillion])
)
# -------------------------DISPLAY-------------------------
# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
'''Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
'''
def go(xShow, fxShow, f, xs):
ys = [xShow(x) for x in xs]
return s + '\n' + '\n'.join(map(
lambda x, y: y + ':\n' + fxShow(f(x)),
xs, ys
))
return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
xShow, fxShow, f, xs
)
# -------------------------GENERAL-------------------------
# isPerfectSquare :: Int -> Bool
def isPerfectSquare(n):
'''True if n is a perfect square.'''
return sqrt(n).is_integer()
# showList :: [a] -> String
def showList(xs):
'''Compact stringification of any list value.'''
return '[' + ','.join(repr(x) for x in xs) + ']' if (
isinstance(xs, list)
) else repr(xs)
# take :: Int -> [a] -> [a]
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
return lambda xs: list(islice(xs, n))
# MAIN ---
if __name__ == '__main__':
main()</syntaxhighlight>
{{Out}}
<pre>OEIS A000037
First 22 terms:
[2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27]
True if any of the first 10^6 terms are perfect squares:
False</pre>
=={{header|Quackery}}==
<syntaxhighlight lang="quackery"> $ "bigrat.qky" loadfile
[ dup n->v 2 vsqrt
drop 1 2 v+ / + ] is nonsquare ( n --> n )
[ sqrt nip 0 = ] is squarenum ( n --> b )
say "Non-squares: "
22 times [ i^ 1+ nonsquare echo sp ]
cr cr
0
999999 times
[ i^ 1+ nonsquare
squarenum if 1+ ]
echo say " square numbers found"</syntaxhighlight>
{{out}}
<pre>Non-squares: 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
0 square numbers found
</pre>
=={{header|R}}==
Printing the first 22 nonsquares.
<
nonsqr(1:22)</
[1] 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
Testing the first million nonsquares.
<
{
sqrx <- sqrt(x)
Line 1,584 ⟶ 2,680:
err < 100*.Machine$double.eps
}
any(is.square(nonsqr(1:1e6)))</
[1] FALSE
=={{header|Racket}}==
<
#lang racket
Line 1,601 ⟶ 2,697:
(for/or ([n (in-range 1 1000001)])
(square? (non-square n)))
</syntaxhighlight>
{{out}}
Line 1,607 ⟶ 2,703:
'(2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27)
#f
</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2016.07}}
<syntaxhighlight lang="raku" line>sub nth-term (Int $n) { $n + round sqrt $n }
# Print the first 22 values of the sequence
say (nth-term $_ for 1 .. 22);
# Check that the first million values of the sequence are indeed non-square
for 1 .. 1_000_000 -> $i {
say "Oops, nth-term($i) is square!" if (sqrt nth-term $i) %% 1;
}</syntaxhighlight>
{{out}}
<pre>(2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27)</pre>
=={{header|Red}}==
<syntaxhighlight lang="rebol">Red ["Sequence of non-squares"]
repeat i 999'999 [
n: i + round/floor 0.5 + sqrt i
if i < 23 [prin [to-integer n ""]]
if equal? round/floor n sqrt n [
print "Square found!"
break
]
]</syntaxhighlight>
{{out}}
<pre>
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
</pre>
=={{header|REXX}}==
REXX has no native support for '''floor''' or '''sqrt''', so these subroutines (functionsa) are written in REXX and are included below.
The '''iSqrt''' is a special integer square root function, it returns the ''integer'' root (and uses no floating point).
:::*
:::* 8 =
:::* 8 = iSqrt(65)
<syntaxhighlight lang="rexx">/*REXX pgm displays some non─square numbers, & also displays a validation check up to 1M*/
parse arg N M . /*obtain optional arguments from the CL*/
if N=='' | N=="," then N= 22 /*Not specified? Then use the default.*/
if M=='' | M=="," then M= 1000000 /* " " " " " " */
say 'The first ' N " non─square numbers:" /*display a header of what's to come. */
say /* [↑] default for M is one million.*/
say center('index', 20) center("non─square numbers", 20)
say center('' , 20, "═") center('' , 20, "═")
do j=1 for N
say center(j, 20) center(j +floor(1/2 +sqrt(j)), 20)
end /*j*/
do k=1 for
iRoot= iSqrt($) /*··· and also use the ISQRT function.*/
if
end /*k*/
say; if #==0 then #= 'no' /*use gooder English for display below.*/
say
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
floor: parse arg floor_; return trunc( floor_ - (floor_ < 0) )
/*──────────────────────────────────────────────────────────────────────────────────────*/
iSqrt: procedure; parse arg x; #=1; r= 0; do while
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_%2
{{out|output}}
<pre>
The first 22 non─square numbers:
index non─square numbers
════════════════════ ════════════════════
1 2
2 3
3 5
4 6
5 7
6 8
7 10
8 11
9 12
10 13
11 14
12 15
13 17
14 18
15 19
16 20
17 21
18 22
19 23
20 24
21 26
22 27
Using the formula: floor[ 1/2 + sqrt(n) ], no squares found up to 1000000.
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
for n=1 to 22
x = n + floor(1/2 + sqrt(n))
see "" + x + " "
next
see nl
</syntaxhighlight>
=={{header|RPL}}==
{{works with|Halcyon Calc|4.2.7}}
≪ DUP √ 0.5 + FLOOR + ≫ ‘'''A0037'''’ STO
≪ 0 ROT ROT '''FOR''' n
'''IF''' n '''A0037''' √ FP NOT '''THEN''' 1 + '''END'''
'''NEXT''' →STR " square(s) found" +
≫ ‘'''TEST'''’ STO
2 runs were necessary to test one million numbers without waking emulator's timedog up.
≪ 1 22 '''FOR''' n n '''A0037''' + '''NEXT''' ≫ EVAL
1 500000 '''TEST'''
500001 1000000 '''TEST'''
{{out}}
<pre>
3: { 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27 }
2: “0 square(s) found“
1: “0 square(s) found“
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang
n + (0.5 + Math.sqrt(n)).floor
end
(1..22).each { |n|
non_squares = (1..1_000_000).map { |n| f(n) }
squares = (1..1001).map { |n| n**2 } # Note: 1001*1001 = 1_002_001 > 1_001_000 = f(1_000_000)
(squares & non_squares).each do |n|
end</
=={{header|Rust}}==
{{works with|Rust|1.1}}
<
fn f(n: i64) -> i64 {
n + (0.5 + (n as f64).sqrt()) as i64
Line 1,698 ⟶ 2,866:
println!("{} unexpected squares found", count);
}
</syntaxhighlight>
=={{header|Scala}}==
<
for(n<-1 to 22) println(n + " "+ nonsqr(n))
Line 1,709 ⟶ 2,877:
j==math.floor(j)
}
println("squares up to one million="+test)</
=={{header|Scheme}}==
<
(lambda (index)
(+ index (inexact->exact (floor (+ (/ 1 2) (sqrt index)))))))
Line 1,742 ⟶ 2,910:
(display ((any? square?) (((sequence non-squares) 1) 999999)))
(newline)</
{{out}}
(2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27)
Line 1,748 ⟶ 2,916:
=={{header|Seed7}}==
<
include "float.s7i";
include "math.s7i";
Line 1,773 ⟶ 2,941:
end if;
end for;
end func;</
=={{header|SETL}}==
<syntaxhighlight lang="setl">program sequence_of_non_squares;
print([nonsquare n : n in [1..22]]);
if exists n in [1..1000000] | is_square nonsquare n then
print("Found square", nonsquare n, "at", n);
else
print("No squares found up to 1 million");
end if;
op is_square(n);
return (floor sqrt n)**2 = n;
end op;
op nonsquare(n);
return n + floor(0.5 + sqrt n);
end op;
end program;</syntaxhighlight>
{{out}}
<pre>[2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27]
No squares found up to 1 million</pre>
=={{header|Sidef}}==
<
{ |i|
if (nonsqr(i).
die "Found a square in the sequence: #{i}"
}
=={{header|Smalltalk}}==
<syntaxhighlight lang="smalltalk">| nonSquare isSquare squaresFound |
nonSquare := [:n |
n + (n sqrt) rounded
].
isSquare := [:n |
n = (((n sqrt) asInteger) raisedTo: 2)
].
Transcript show: 'The first few non-squares:'; cr.
1 to: 22 do: [:n |
Transcript show: (nonSquare value: n) asString; cr
].
squaresFound := 0.
1 to: 1000000 do: [:n |
(isSquare value: (nonSquare value: n)) ifTrue: [
squaresFound := squaresFound + 1
]
].
Transcript show: 'Squares found for values up to 1,000,000: ';
show: squaresFound asString; cr</syntaxhighlight>
=={{header|SparForte}}==
As a structured script.
<syntaxhighlight lang="ada">#!/usr/local/bin/spar
pragma annotate( summary, "nonsquares" );
pragma annotate( description, "Show that the following remarkable formula gives the" );
pragma annotate( description, "sequence of non-square natural numbers: n +" );
pragma annotate( description, "floor(1/2 + sqrt(n)). Print out the values for n in" );
pragma annotate( description, "the range 1 to 22. Show that no squares occur for n" );
pragma annotate( description, "less than one million." );
pragma annotate( see_also, "http://rosettacode.org/wiki/Sequence_of_non-squares" );
pragma annotate( author, "Ken O. Burtch" );
pragma license( unrestricted );
pragma restriction( no_external_commands );
procedure nonsquares is
function is_non_square (n : positive) return positive is
begin
return n + positive (numerics.rounding(numerics.sqrt (long_float (n))));
end is_non_square;
i : positive;
begin
for n in 1..22 loop -- First 22 non-squares
put (strings.image (is_non_square (n)));
end loop;
new_line;
for n in 1..1_000_000 loop -- Check first million of
i := is_non_square (n);
if i = positive (numerics.rounding(numerics.sqrt (long_float (i))))**2 then
put_line ("Found a square:" & strings.image (n));
end if;
end loop;
end nonsquares;</syntaxhighlight>
=={{header|Standard ML}}==
<
val nonsqr = fn : int -> int
- List.tabulate (23, nonsqr);
Line 1,797 ⟶ 3,044:
loop 1
end;
val it = true : bool</
=={{header|Tcl}}==
<
set f {n {expr {$n + floor(0.5 + sqrt($n))}}}
Line 1,816 ⟶ 3,063:
}
}
puts "done"</
{{out}}
<pre>1 2.0
Line 1,847 ⟶ 3,094:
Definition and 1 to 22, interactively:
<
Done
■ seq(f(n),n,1,22)
{2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27}</
Program testing up to one million:
<
Prgm
Local i, ns
Line 1,864 ⟶ 3,111:
EndFor
Disp "Done"
EndPrgm</
(This program has not been run to completion.)
=={{header|Transd}}==
<syntaxhighlight lang="scheme">#lang transd
MainModule: {
nonsqr: (λ i Int()
(ret (+ i (to-Int (floor (+ 0.5 (sqrt i))))))),
_start: (lambda locals: d Double()
(for i in Range(1 23) do
(textout (nonsqr i) " "))
(for i in Range(1 1000001) do
(= d (sqrt (nonsqr i)))
(if (eq d (floor d))
(throw String("Square: " i))))
(textout "\n\nUp to 1 000 000 - no squares found.")
)
}</syntaxhighlight>
{{out}}
<pre>
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
Up to 1 000 000 - no squares found.
</pre>
=={{header|True BASIC}}==
<syntaxhighlight lang="qbasic">FUNCTION nonSquare (n)
LET nonSquare = n + INT(0.5 + SQR(n))
END FUNCTION
! Display first 22 values
PRINT "The first 22 numbers generated by the sequence are : "
FOR i = 1 TO 22
PRINT nonSquare(i); " ";
NEXT i
PRINT
! Check FOR squares up TO one million
LET found = 0
FOR i = 1 TO 1e6
LET j = SQR(nonSquare(i))
IF j = INT(j) THEN
LET found = 1
PRINT i, " square numbers found"
EXIT FOR
END IF
NEXT i
IF found = 0 THEN PRINT "No squares found"
END</syntaxhighlight>
=={{header|Ursala}}==
<
#import flo
Line 1,878 ⟶ 3,177:
examples = %neALP ^(~&,nth_non_square)*t iota23
check = (is_square*~+nth_non_square*t; ~&i&& %eLP)||-[no squares found]-! iota 1000000</
{{out}}
<pre>
Line 1,906 ⟶ 3,205:
no squares found
</pre>
=={{header|VBA}}==
<syntaxhighlight lang="vb">
Sub Main()
Dim i&, c&, j#, s$
Const N& = 1000000
s = "values for n in the range 1 to 22 : "
For i = 1 To 22
s = s & ns(i) & ", "
Next
For i = 1 To N
j = Sqr(ns(i))
If j = CInt(j) Then c = c + 1
Next
Debug.Print s
Debug.Print c & " squares less than " & N
End Sub
Private Function ns(l As Long) As Long
ns = l + Int(1 / 2 + Sqr(l))
End Function</syntaxhighlight>
{{out}}
<pre>values for n in the range 1 to 22 : 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27,
0 squares less than 1000000</pre>
=={{header|Wren}}==
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./fmt" for Fmt
System.print("The first 22 numbers in the sequence are:")
System.print(" n term")
for (n in 1...1e6) {
var s = n + (0.5 + n.sqrt).floor
var ss = s.sqrt.round
if (ss * ss == s) {
Fmt.print("The $r number in the sequence $d = $d x $d is a square.", n, s, ss, ss)
return
}
if (n <= 22) Fmt.print(" $2d $2d", n, s)
}
System.print("\nNo squares were found in the first 999,999 terms.")</syntaxhighlight>
{{out}}
<pre>
The first 22 numbers in the sequence are:
n term
1 2
2 3
3 5
4 6
5 7
6 8
7 10
8 11
9 12
10 13
11 14
12 15
13 17
14 18
15 19
16 20
17 21
18 22
19 23
20 24
21 26
22 27
No squares were found in the first 999,999 terms.
</pre>
=={{header|XLISP}}==
<syntaxhighlight lang="lisp">(defun non-square (n)
(+ n (floor (+ 0.5 (sqrt n)))))
(defun range (x y)
(if (< x y)
(cons x (range (+ x 1) y))))
(defun squarep (x)
(= x (expt (floor (sqrt x)) 2)))
(defun count-squares (x y)
(define squares 0)
(if (squarep (non-square x))
(define squares (+ squares 1)))
(if (= x y)
squares
(count-squares (+ x 1) y)))
(print (mapcar non-square (range 1 23)))
(print `(number of squares for values less than 1000000 = ,(count-squares 1 1000000)))</syntaxhighlight>
{{out}}
<pre>(2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27)
(NUMBER OF SQUARES FOR VALUES LESS THAN 1000000 = 0)</pre>
=={{header|XPL0}}==
<
func real Floor(X); \Truncate X toward - infinity
Line 1,930 ⟶ 3,327:
M0:= M;
];
]</
{{out}}
Line 1,936 ⟶ 3,333:
2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27
</pre>
=={{header|Yabasic}}==
<syntaxhighlight lang="yabasic">// Display first 22 values
print "The first 22 numbers generated by the sequence are : "
for i = 1 to 22
print nonSquare(i), " ";
next i
print
// Check for squares up to one million
found = false
for i = 1 to 1e6
j = sqrt(nonSquare(i))
if j = int(j) then
found = true
print i, " square numbers found" //print "Found square: ", i
break
end if
next i
if not found print "No squares found"
end
sub nonSquare (n)
return n + int(0.5 + sqrt(n))
end sub</syntaxhighlight>
=={{header|zkl}}==
<
[1..22].apply(seq).toString(*).println();
Line 1,944 ⟶ 3,368:
isSquare(25) //-->True
isSquare(26) //-->False
[2..0d1_000_000].filter(fcn(n){isSquare(seq(n))}).println();</
modf returns the integer and fractional parts of a float
{{out}}
| |||