Upside-down numbers: Difference between revisions
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;* [[oeis:A299539|OEIS:A299539 - Upside-down numbers]]
=={{header|ALGOL 68}}==
{{Trans|Phix}}
Assumes <code>LONG INT</code> is at least 64 bits.
<syntaxhighlight lang="algol68">
BEGIN # find and count upside-down numbers - translation of Phix #
PROC get counts = ( INT d, REF LONG INT first, last )LONG INT:
BEGIN
LONG INT count := first := last := 1;
FOR i FROM 2 TO d DO
first := last + 1;
IF NOT ODD i THEN count *:= 9 FI;
last := first + count - 1
OD;
count
END # get counts # ;
PROC kth of n = ( LONG INT kth, digits, count )STRING:
IF digits = 0 THEN ""
ELIF digits = 1 THEN "5"
ELSE
OP D = ( INT n )CHAR: REPR ( ABS "0" + n );
LONG INT reduced count := count OVER 9;
INT d = SHORTEN ( ( kth - 1 ) OVER reduced count );
D ( 1 + d ) + kth of n( kth - ( d * reduced count ), digits - 2, reduced count ) + D ( 9 - d )
FI # kth of n # ;
PROC get which = ( LONG INT nth in, REF LONG INT count, first, last, kth, digits )STRING:
BEGIN
LONG INT nth := nth in;
digits := count := first := last := 1;
WHILE nth > last DO
first := last + 1;
digits +:= 1;
IF NOT ODD digits THEN count *:= 9 FI;
last := first + count - 1
OD;
kth := nth - first + 1;
kth of n( kth, digits, count )
END # get which # ;
PROC ord = ( LONG INT n )STRING:
IF INT d2 = SHORTEN ( n MOD 100 );
d2 >= 10 AND d2 <= 20
THEN "th"
ELSE CASE SHORTEN ( n MOD 10 ) IN "st", "nd", "rd" OUT "th" ESAC
FI # ord # ;
print( ( "The first 50 upside down numbers:", newline ) );
FOR i TO 50 DO
STRING ud := get which( i
, LOC LONG INT, LOC LONG INT, LOC LONG INT
, LOC LONG INT, LOC LONG INT
);
WHILE ( UPB ud - LWB ud ) < 3 DO " " +=: ud OD;
print( ( ud, IF i MOD 10 /= 0 THEN " " ELSE newline FI ) )
OD;
print( ( newline ) );
FOR d TO 7 DO
LONG INT first := 0, ord first := 0, last := 0, ord last := 0;
LONG INT count = get counts( d, first, last );
print( ( "There are ", whole( count, 0 ), " ", whole( d, 0 )
, "-digit upside down numbers (the "
, whole( first, 0 ), ord( first ), " to ", whole( last, 0 ), ord( last )
, ")", newline
)
)
OD;
print( ( "(etc...)", newline, newline ) );
[]LONG INT position = ( 1, 2, 10, 11, 182, 500, 910, 911
, 5 000, 50 000, 500 000, 5 000 000, 50 000 000
, 500 000 000, 5 000 000 000, 50 000 000 000, 500 000 000 000
, 5 000 000 000 000, 50 000 000 000 000, 500 000 000 000 000
, 5 000 000 000 000 000
);
FOR i FROM LWB position TO UPB position DO
LONG INT w = position[ i ];
LONG INT count := 0, first := 0, last := 0, kth := 0, digits := 0;
STRING res = get which( w, count, first, last, kth, digits );
print( ( "The ", whole( w, 0 ), ord( w ), " upside down number"
, " is the ", whole( kth, 0 ), ord( kth ), " ", whole( digits, 0 )
, "-digit number (", res, ")", newline
)
)
OD
END
</syntaxhighlight>
{{out}}
<pre>
The first 50 upside down numbers:
5 19 28 37 46 55 64 73 82 91
159 258 357 456 555 654 753 852 951 1199
1289 1379 1469 1559 1649 1739 1829 1919 2198 2288
2378 2468 2558 2648 2738 2828 2918 3197 3287 3377
3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
There are 1 1-digit upside down numbers (the 1st to 1st)
There are 9 2-digit upside down numbers (the 2nd to 10th)
There are 9 3-digit upside down numbers (the 11th to 19th)
There are 81 4-digit upside down numbers (the 20th to 100th)
There are 81 5-digit upside down numbers (the 101st to 181st)
There are 729 6-digit upside down numbers (the 182nd to 910th)
There are 729 7-digit upside down numbers (the 911th to 1639th)
(etc...)
The 1st upside down number is the 1st 1-digit number (5)
The 2nd upside down number is the 1st 2-digit number (19)
The 10th upside down number is the 9th 2-digit number (91)
The 11th upside down number is the 1st 3-digit number (159)
The 182nd upside down number is the 1st 6-digit number (111999)
The 500th upside down number is the 319th 6-digit number (494616)
The 910th upside down number is the 729th 6-digit number (999111)
The 911th upside down number is the 1st 7-digit number (1115999)
The 5000th upside down number is the 3361st 8-digit number (56546545)
The 50000th upside down number is the 35239th 10-digit number (6441469664)
The 500000th upside down number is the 367141st 12-digit number (729664644183)
The 5000000th upside down number is the 3804259th 14-digit number (82485246852682)
The 50000000th upside down number is the 39238321st 16-digit number (9285587463255281)
The 500000000th upside down number is the 15724390th 19-digit number (1436368345672474769)
The 5000000000th upside down number is the 641519500th 21-digit number (269222738456273888148)
The 50000000000th upside down number is the 10773675490th 23-digit number (41835623444566678457296)
The 500000000000th upside down number is the 146963079400th 25-digit number (5724139689945611241796835)
The 5000000000000th upside down number is the 1822667714590th 27-digit number (751766588225456588225443953)
The 50000000000000th upside down number is the 21404009431300th 29-digit number (94816546925914569158146549261)
The 500000000000000th upside down number is the 36744952787041st 32-digit number (12651942383972646483172786195489)
The 5000000000000000th upside down number is the 830704575083359th 34-digit number (1513835774459212468981566335727959)
</pre>
=={{header|Basic}}==
==={{header|Applesoft BASIC}}===
Beyond 9 digits, rounding errors occur.
<syntaxhighlight lang="basic"> 1 PRINT "THE FIRST 50 UPSIDE DOWN NUMBERS:": FOR I = 1 TO 50: GOSUB 4: NEXT I: PRINT
2 FOR J = 2 TO 10::I = INT (5 * 10 ^ J): PRINT CHR$ (13)I"TH: ";: GOSUB 4: NEXT J
3 END
4 GOSUB 5: PRINT O$;: RETURN
5 IF I > = 1E9 THEN PRINT "?OVERFLOW" + CHR$ (7): END
6 L$ = "":R$ = "":S = I - 1:F = 1:I$(1) = "5": FOR E = 0 TO 1E38: FOR O = F TO 1:R = S:S = S - INT (9 ^ E):F = 0: IF S > = 0 THEN NEXT O,E
7 IF E THEN R = R + .5: FOR D = E - 1 TO 0 STEP - 1:N = INT (R / 9 ^ D):L$ = L$ + STR$ (N + 1):R$ = STR$ (9 - N) + R$:R = R - N * INT (9 ^ D): NEXT D
8 O$ = L$ + I$(O) + R$ + " "
9 RETURN
</syntaxhighlight>
{{out}}
<pre>THE FIRST 50 UPSIDE DOWN NUMBERS:
5 19 28 37 46 55 64 73 82 91 159 258 357 456 555 654 753 852 951 1199 1289 1379 1469 1559 1649 1739 1829 1919 2198 2288 2378 2468 2558 2648 2738 2828 2918 3197 3287 3377 3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
500TH: 494616
5000TH: 56546545
50000TH: 6441469664
500000TH: 729664644183
5000000TH: 82485246852682
50000000TH: 9285587463255281
500000000TH: 1436368345672474769
5E+09TH: ?OVERFLOW
</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">
function is_ups( n as uinteger ) as boolean
dim as string m = str(n)
dim as uinteger lm = len(m), i
for i = 1 to int(lm/2.0+0.5)
if val(mid(m,i,1)) + val(mid(m,lm-i+1,1)) <> 10 then return false
next i
return true
end function
dim as uinteger count, n=0
while count<5000001
if is_ups(n) then
count = count + 1
if count < 51 then
print n,
if count mod 5 = 0 then print
end if
if count = 500 or count = 5000 then
print n
end if
end if
n = n + 1
wend
</syntaxhighlight>
<pre>
5 19 28 37 46
55 64 73 82 91
159 258 357 456 555
654 753 852 951 1199
1289 1379 1469 1559 1649
1739 1829 1919 2198 2288
2378 2468 2558 2648 2738
2828 2918 3197 3287 3377
3467 3557 3647 3737 3827
3917 4196 4286 4376 4466
494616
56546545
</pre>
=={{header|C++}}==
<syntaxhighlight lang="C++">#include <iostream>
#include <vector>
#include <algorithm>
bool isUpsideDown( int n ) {
std::vector<int> digits ;
while ( n != 0 ) {
digits.push_back( n % 10 ) ;
n /= 10 ;
}
if ( std::find ( digits.begin( ) , digits.end( ) , 0 ) != digits.end( ) )
return false ;
int forward = 0 ;
int backward = digits.size( ) - 1 ;
while ( forward <= backward ) {
if ( digits[forward] + digits[backward] != 10 )
return false ;
forward++ ;
if ( backward > 0 ) {
backward-- ;
}
}
return true ;
}
int main( ) {
int current = 0 ;
int sum = 0 ;
std::vector<int> solution ;
while ( sum != 5000 ) {
current++ ;
if ( isUpsideDown( current ) ) {
solution.push_back( current ) ;
sum++ ;
}
}
std::cout << "The first 50 upside-down numbers:\n" ;
std::cout << "(" ;
for ( int i = 0 ; i < 50 ; i++ )
std::cout << solution[ i ] << ' ' ;
std::cout << ")\n" ;
std::cout << "The five hundredth such number: " << solution[499] << '\n' ;
std::cout << "The five thousandth such number: " << solution[4999] << '\n' ;
return 0 ;
}</syntaxhighlight>
{{out}}
<pre>
The first 50 upside-down numbers:
(5 19 28 37 46 55 64 73 82 91 159 258 357 456 555 654 753 852 951 1199 1289 1379 1469 1559 1649 1739 1829 1919 2198 2288 2378 2468 2558 2648 2738 2828 2918 3197 3287 3377 3467 3557 3647 3737 3827 3917 4196 4286 4376 4466 )
The five hundredth such number: 494616
The five thousandth such number: 56546545
</pre>
=={{header|Go}}==
Line 136 ⟶ 383:
50,000,000th : 9,285,587,463,255,281
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
function IsUpsideDown(N: integer): boolean;
{Test if N is upsidedown number}
var I,J: integer;
var IA: TIntegerDynArray;
begin
Result:=False;
{Get all digits in the number}
GetDigits(N,IA);
for I:=0 to Length(IA) div 2 do
begin
{Index to right side of number}
J:=High(IA)-I;
{do left and right side add up to 10?}
if IA[J]+IA[I]<>10 then exit;
{No zeros allowed}
if (IA[J]=0) or (IA[I]=0) then exit;
end;
Result:=True;
end;
procedure ShowUpsideDownNumbers(Memo: TMemo);
var I,J,K: integer;
var Cnt: integer;
var S: string;
begin
Cnt:=0;
S:='';
{Show first 50 upside down numbers}
for I:=5 to high(integer) do
if IsUpsideDown(I) then
begin
Inc(Cnt);
S:=S+Format('%5d',[I]);
if (Cnt mod 10)=0 then S:=S+CRLF;
if Cnt=50 then break;
end;
Memo.Lines.Add(S);
{Show 500th, and 5,000th }
for I:=I to high(integer) do
if IsUpsideDown(I) then
begin
Inc(Cnt);
case Cnt of
500: Memo.Lines.Add(Format(' 500th Upsidedown = %10.0n',[I+0.0]));
5000: Memo.Lines.Add(Format('5,000th Upsidedown = %10.0n',[I+0.0]));
end;
if Cnt>5000 then break;
end;
end;
</syntaxhighlight>
{{out}}
<pre>
5 19 28 37 46 55 64 73 82 91
159 258 357 456 555 654 753 852 951 1199
1289 1379 1469 1559 1649 1739 1829 1919 2198 2288
2378 2468 2558 2648 2738 2828 2918 3197 3287 3377
3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
500th Upsidedown = 493,716
5,000th Upsidedown = 56,537,545
Elapsed Time: 10.141 Sec.
</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="Haskell">import Data.Char ( digitToInt )
import Data.List ( unfoldr , (!!) )
findLimits :: (Int , Int) -> [(Int , Int)]
findLimits (st , end ) = unfoldr(\(x , y ) -> if x > y then Nothing else
Just ((x , y ) , (x + 1 , y - 1 ))) (st , end )
isUpsideDown :: Int -> Bool
isUpsideDown n
|elem '0' str = False
|otherwise = all (\(a , b ) -> digitToInt( str !! a ) + digitToInt ( str !!
b ) == 10 ) $ findLimits ( 0 , length str - 1 )
where
str = show n
main :: IO ( )
main = do
let upsideDowns = take 5000 $ filter isUpsideDown [1..]
putStrLn "The first fifty upside-down numbers!"
print $ take 50 upsideDowns
putStr "The five hundredth such number : "
print $ upsideDowns !! 499
putStr "The five thousandth such number : "
print $ last upsideDowns</syntaxhighlight>
{{out}}
<pre>
The first fifty upside-down numbers!
[5,19,28,37,46,55,64,73,82,91,159,258,357,456,555,654,753,852,951,1199,1289,1379,1469,1559,1649,1739,1829,1919,2198,2288,2378,2468,2558,2648,2738,2828,2918,3197,3287,3377,3467,3557,3647,3737,3827,3917,4196,4286,4376,4466]
The five hundredth such number : 494616
The five thousandth such number : 56546545
</pre>
=={{header|jq}}==
Line 283 ⟶ 641:
Five millionth: 82,485,246,852,682
</pre>
=={{header|Nim}}==
{{trans|Python}}
<syntaxhighlight lang="Nim">import std/[math, strformat, strutils, sugar]
iterator upsideDownNumbers(): (int, int) =
## Generate upside-down numbers (OEIS A299539).
const
Wrappings = [(1, 9), (2, 8), (3, 7), (4, 6),
(5, 5), (6, 4), (7, 3), (8, 2), (9, 1)]
var
evens = @[19, 28, 37, 46, 55, 64, 73, 82, 91]
odds = @[5]
oddIndex, evenIndex = 0
ndigits = 1
count = 0
while true:
if ndigits mod 2 == 1:
if odds.len > oddIndex:
inc count
yield (count, odds[oddIndex])
inc oddIndex
else:
# Build next odds, but switch to evens.
odds = collect:
for (hi, lo) in Wrappings:
for i in odds:
hi * 10^(ndigits + 1) + 10 * i + lo
inc ndigits
oddIndex = 0
else:
if evens.len > evenIndex:
inc count
yield (count, evens[evenIndex])
inc evenIndex
else:
# Build next evens, but switch to odds.
evens = collect:
for (hi, lo) in Wrappings:
for i in evens:
hi * 10^(ndigits + 1) + 10 * i + lo
inc ndigits
evenIndex = 0
echo "First fifty upside-downs:"
for (udcount, udnumber) in upsideDownNumbers():
if udcount <= 50:
stdout.write &"{udnumber:5}"
if udcount mod 10 == 0: echo()
elif udcount == 500:
echo &"\nFive hundredth: {insertSep($udnumber)}"
elif udcount == 5_000:
echo &"Five thousandth: {insertSep($udnumber)}"
elif udcount == 50_000:
echo &"Fifty thousandth: {insertSep($udnumber)}"
elif udcount == 500_000:
echo &"Five hundred thousandth: {insertSep($udnumber):}"
elif udcount == 5_000_000:
echo &"Five millionth: {insertSep($udnumber):}"
break
</syntaxhighlight>
{{out}}
<pre>First fifty upside-downs:
5 19 28 37 46 55 64 73 82 91
159 258 357 456 555 654 753 852 951 1199
1289 1379 1469 1559 1649 1739 1829 1919 2198 2288
2378 2468 2558 2648 2738 2828 2918 3197 3287 3377
3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
Five hundredth: 494_616
Five thousandth: 56_546_545
Fifty thousandth: 6_441_469_664
Five hundred thousandth: 729_664_644_183
Five millionth: 82_485_246_852_682</pre>
=={{header|Pascal}}==
Line 471 ⟶ 905:
Real time: 0.271 s CPU share: 99.00 %
</pre>
=={{header|Perl}}==
<syntaxhighlight lang="perl" line>use v5.36;
use Lingua::EN::Numbers qw(num2en_ordinal);
sub comma { reverse ((reverse shift) =~ s/(.{3})/$1,/gr) =~ s/^,//r }
sub table ($c, @V) { my $t = $c * (my $w = 5); ( sprintf( ('%'.$w.'d')x@V, @V) ) =~ s/.{1,$t}\K/\n/gr }
sub updown ($n) {
my($i,@ud);
while (++$i) {
next if subset($i, '0', 0) or 0 != ($i+reverse $i) % 10;
my @i = split '', $i;
next if grep { 10 != $i[$_] + $i[$#i-$_] } 0..$#i;
push @ud, $i;
last if $n == @ud;
}
@ud
}
my @ud = updown( 5000 );
say "First fifty upside-downs:\n" . table 10, @ud[0..49];
say ucfirst num2en_ordinal($_) . ': ' . comma $ud[$_-1] for 500, 5000;</syntaxhighlight>
{{out}}
<pre>First fifty upside-downs:
5 19 28 37 46 55 64 73 82 91
159 258 357 456 555 654 753 852 951 1199
1289 1379 1469 1559 1649 1739 1829 1919 2198 2288
2378 2468 2558 2648 2738 2828 2918 3197 3287 3377
3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
Five hundredth: 494,616
Five thousandth: 56,546,545</pre>
=={{header|Phix}}==
Finishes instantly
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_counts</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">d</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">last</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">*=</span><span style="color: #000000;">9</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">first</span><span style="color: #0000FF;">+</span><span style="color: #000000;">count</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">first</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first</span><span style="color: #0000FF;">),</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">last</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">""</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (might as well check)</span>
<span style="color: #008080;">return</span> <span style="color: #008000;">"5"</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">9</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">kth</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">*</span><span style="color: #000000;">count</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'1'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'9'</span><span style="color: #0000FF;">-</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">></span><span style="color: #000000;">last</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">last</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">digits</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">*=</span><span style="color: #000000;">9</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">first</span><span style="color: #0000FF;">+</span><span style="color: #000000;">count</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">kth</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">-</span><span style="color: #000000;">first</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"The first 50 upside down numbers:\n%s\n"</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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">50</span><span style="color: #0000FF;">),</span><span style="color: #000000;">get_which</span><span style="color: #0000FF;">),</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%4s"</span><span style="color: #0000FF;">))</span>
<span style="color: #000080;font-style:italic;">-- Let's just spell it out for you...</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"There are %,d %d-digit upside down numbers (the %,d%s to %,d%s)\n"</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">7</span> <span style="color: #008080;">do</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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">get_counts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</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;">"(etc...)\n\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"The %,d%s upside down number is the %,d%s %d-digit number (%s)\n"</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span> <span style="color: #008080;">in</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: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">182</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500</span><span style="color: #0000FF;">,</span><span style="color: #000000;">910</span><span style="color: #0000FF;">,</span><span style="color: #000000;">911</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">500000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">50000000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500000000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000000000000</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"The total time taken for this onerous and difficult task: %s\n"</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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">))</span>
<!--</syntaxhighlight>-->
{{out}}
<pre style="font-size: 12px">
The first 50 upside down numbers:
5 19 28 37 46 55 64 73 82 91
159 258 357 456 555 654 753 852 951 1199
1289 1379 1469 1559 1649 1739 1829 1919 2198 2288
2378 2468 2558 2648 2738 2828 2918 3197 3287 3377
3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
There are 1 1-digit upside down numbers (the 1st to 1st)
There are 9 2-digit upside down numbers (the 2nd to 10th)
There are 9 3-digit upside down numbers (the 11th to 19th)
There are 81 4-digit upside down numbers (the 20th to 100th)
There are 81 5-digit upside down numbers (the 101st to 181st)
There are 729 6-digit upside down numbers (the 182nd to 910th)
There are 729 7-digit upside down numbers (the 911th to 1,639th)
(etc...)
The 1st upside down number is the 1st 1-digit number (5)
The 2nd upside down number is the 1st 2-digit number (19)
The 10th upside down number is the 9th 2-digit number (91)
The 11th upside down number is the 1st 3-digit number (159)
The 182nd upside down number is the 1st 6-digit number (111999)
The 500th upside down number is the 319th 6-digit number (494616)
The 910th upside down number is the 729th 6-digit number (999111)
The 911th upside down number is the 1st 7-digit number (1115999)
The 5,000th upside down number is the 3,361st 8-digit number (56546545)
The 50,000th upside down number is the 35,239th 10-digit number (6441469664)
The 500,000th upside down number is the 367,141st 12-digit number (729664644183)
The 5,000,000th upside down number is the 3,804,259th 14-digit number (82485246852682)
The 50,000,000th upside down number is the 39,238,321st 16-digit number (9285587463255281)
The 500,000,000th upside down number is the 15,724,390th 19-digit number (1436368345672474769)
The 5,000,000,000th upside down number is the 641,519,500th 21-digit number (269222738456273888148)
The 50,000,000,000th upside down number is the 10,773,675,490th 23-digit number (41835623444566678457296)
The 500,000,000,000th upside down number is the 146,963,079,400th 25-digit number (5724139689945611241796835)
The 5,000,000,000,000th upside down number is the 1,822,667,714,590th 27-digit number (751766588225456588225443953)
The 50,000,000,000,000th upside down number is the 21,404,009,431,300th 29-digit number (94816546925914569158146549261)
The 500,000,000,000,000th upside down number is the 36,744,952,787,041st 32-digit number (12651942383972646483172786195489)
The 5,000,000,000,000,000th upside down number is the 830,704,575,083,359th 34-digit number (1513835774459212468981566335727959)
The total time taken for this onerous and difficult task: 0s
</pre>
=== higher limits ===
Limited to the ''18,446,744,073,709,551,614th?'', we can do better than that!
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> <span style="color: #000080;font-style:italic;">-- (so that nth etc can exceed 64 bits of precision)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">""</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">"5"</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">mpz_divexact_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">dz</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">mpz_fdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_add_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'1'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'9'</span><span style="color: #0000FF;">-</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">)></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpz_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">digits</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">first</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">kth</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">first</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</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;">"The %sth upside down number is\n %s (%s)\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1e100"</span><span style="color: #0000FF;">)))</span>
<!--</syntaxhighlight>-->
{{out}}
<pre style="font-size: 7px">
The 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000th upside down number is
454594394343883179243759282183821923122343988685136868482218367266879951778395152999458916423484426556989121455486626786491256111859517233951132448347298826242479524221767889781982729828153768139722767617615656 (0.0s)
</pre>
Line 492 ⟶ 1,115:
else:
# build next odds, but switch to evens
odds =
ndigits += 1
odd_index = 0
Line 502 ⟶ 1,125:
else:
# build next evens, but switch to odds
evens =
ndigits += 1
even_index = 0 even_index = 0
Line 542 ⟶ 1,165:
Five millionth: 82,485,246,852,682
</pre>
=={{header|Quackery}}==
(Load extensions for the faster merge sort.)
'''Method'''
Start with generation zero as the empty string and "5". Make the next generation by expanding the previous generation (<code>expand</code>) i.e. wrapping each of the strings in "1" and "9", "2" and "8" … "8" and "2", "9" and "1". Accumulate the generations. The accumulator starts with "5", after one iteration it has "5", "19", "28" … "82", "91", "159", "258" … "852", "951".
Note that this does not produce the numbers in numerical order. It's close to numerical order but not quite there.
So once sufficient numbers have been produced to guarantee that all the numbers in the required range have been calculated, convert them from string format to numerical format and sort, then truncate the list of upside down numbers to the required length.
<code>necessary</code> computes a safe number of items to include in the list to guarantee that none are missing from the truncated list - i.e. the length of the list after each iteration of <code>expand</code>. It is <code>(9^n - 5) / 4</code>, where <code>n</code> is the number of iterations. ([https://oeis.org/A211866 OEIS A211866])
<code>^</code> in <code>necessary</code> is bitwise XOR, not exponentiation.
<syntaxhighlight lang="Quackery"> [ 0
[ 2dup > while
1 ^ 9 * 1+ again ]
nip ] is necessary ( n --> n )
[ [] swap
witheach
[ ' [ [ char 1 char 9 ]
[ char 2 char 8 ]
[ char 3 char 7 ]
[ char 4 char 6 ]
[ char 5 char 5 ]
[ char 6 char 4 ]
[ char 7 char 3 ]
[ char 8 char 2 ]
[ char 9 char 1 ] ]
witheach
[ over dip do
dip swap join
swap join nested
rot swap join
swap ]
drop ] ] is expand ( [ --> [ )
[ dup necessary temp put
' [ [ char 5 ] ]
' [ [ ] [ char 5 ] ]
[ expand tuck join swap
over size
temp share < not
until ]
drop
temp release
[] swap
witheach
[ $->n drop join ]
sort
swap split drop ] is upsidedowns ( n --> [ )
5000 upsidedowns
say "First 50 upside down numbers:"
dup 50 split drop
[] swap witheach
[ number$ nested join ]
45 wrap$
cr cr
say "500th upside down number: "
dup 499 peek echo
cr
say "5000th upside down number: "
4999 peek echo</syntaxhighlight>
{{out}}
<pre>First 50 upside down numbers:
5 19 28 37 46 55 64 73 82 91 159 258 357 456
555 654 753 852 951 1199 1289 1379 1469 1559
1649 1739 1829 1919 2198 2288 2378 2468 2558
2648 2738 2828 2918 3197 3287 3377 3467 3557
3647 3737 3827 3917 4196 4286 4376 4466
500th upside down number: 494616
5000th upside down number: 56546545</pre>
=={{header|Raku}}==
Line 573 ⟶ 1,275:
Five hundred thousandth: 729,664,644,183
Five millionth: 82,485,246,852,682</pre>
=={{header|RPL}}==
{{works with|Halcyon Calc|4.2.8}}
{| class="wikitable"
! RPL code
! Comment
|-
|
≪ 9 SWAP 2 / CEIL ^ ≫ ''''POW92'''' STO
≪
SWAP 1 - "" SWAP 1 4 ROLL START
9 MOD LAST / FLOOR SWAP
1 + →STR ROT + SWAP NEXT DROP
≫ ''''→STR9'''' STO
≪ → str
≪ "" str SIZE 1 FOR j
106 str j DUP SUB NUM - CHR + -1 STEP
≫ ≫ ''''UDSTR'''' STO
≪
IF DUP 1 == THEN DROP "5" ELSE
1 WHILE OVER 1 > REPEAT
SWAP OVER '''POW92''' - SWAP 1 + END
1 - DUP '''POW92''' ROT + 1 - → series order
≪ order series 2 / CEIL '''→STR9''' DUP
IF order 2 MOD NOT THEN "5" + END
SWAP '''UDSTR''' +
≫ END
≫ ''''UPSDN'''' STO
|
'''POW92''' ''( n -- 9^ceil(n/2) ) ''
'''→STR9''' ''( n str_length -- "12..9" ) ''
n-- ; s = "" ; loop size times
n,m = divmod(n)
append "m+1" to s
return s
'''UDSTR''' ''( "str" -- "rts" )''
s = "" ; loop for j from size(str) downto 1
s[j] = 106 - char(ascii(str[j]))
return s
'''UPSDN''' ''( n -- "a(n)" ) ''
if n = 1 then return "5" else
series = 1 ; while n > 1
n -= 9^ceil(series/2); series++
series-- ; order = n + 9^ceil(series/2) + 1
Create left part of the upside-down number, as a string
Add 5 in the middle if appropriate
Add upside-down right part
et voilà
return full string
|}
{{in}}
<pre>
≪ {} 1 50 FOR j j UPSDN+ NEXT ≫ EVAL
500 UPSDN 5000 UPSDN 50000 UPSDN 500000 UPSDN 5000000 UPSDN
5000000000 UPSDN
</pre>
{{out}}
<pre>
7: { "5" "19" "28" "37" "46" "55" "64" "73" "82" "91" "159" "258" "357" "456" "555" "654" "753" "852" "951" "1199" "1289" "1379" "1469" "1559" "1649" "1739" "1829" "1919" "2198" "2288" "2378" "2468" "2558" "2648" "2738" "2828" "2918" "3197" "3287" "3377" "3467" "3557" "3647" "3737" "3827" "3917" "4196" "4286" "4376" "4466" }
6: "494616"
5: "56546545"
4: "6441469664"
3: "729664644183"
2: "82485246852682"
1: "269222738456273888148"
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">DIGITS =(1..9).to_a
updowns = Enumerator.new do |y|
y << 5
(1..).each do |s|
perms = DIGITS.repeated_permutation(s)
perms.each{|perm| y << (perm + perm.reverse.map{|n| 10-n}).join.to_i }
perms.each{|perm| y << (perm + [5] + perm.reverse.map{|n| 10-n}).join.to_i }
end
end
res = updowns.take(5000000)
res.first(50).each_slice(10){|slice| puts "%6d"*slice.size % slice}
puts
n = 500
5.times do
puts "%8d: %-10d" % [n, res[n-1]]
n *= 10
end
</syntaxhighlight>
{{out}}
<pre> 5 19 28 37 46 55 64 73 82 91
159 258 357 456 555 654 753 852 951 1199
1289 1379 1469 1559 1649 1739 1829 1919 2198 2288
2378 2468 2558 2648 2738 2828 2918 3197 3287 3377
3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
500th : 494616
5000th : 56546545
50000th : 6441469664
500000th : 729664644183
5000000th : 82485246852682
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="Rust">fn is_upside_down( num : u32 ) -> bool {
let numberstring : String = num.to_string( ) ;
let len = numberstring.len( ) ;
let numberstr = numberstring.as_str( ) ;
if numberstr.contains( "0" ) {
return false ;
}
if len % 2 == 1 && numberstr.chars( ).nth( len / 2 ).unwrap( ) != '5' {
return false ;
}
let mut forward : usize = 0 ;
let mut backward : usize = len - 1 ;
while forward <= backward {
let first = numberstr.chars( ).nth( forward ).expect("No digit!").
to_digit( 10 ).unwrap( ) ;
let second = numberstr.chars( ).nth( backward ).expect("No digit!").
to_digit( 10 ).unwrap( ) ;
if first + second != 10 {
return false ;
}
forward += 1 ;
if backward != 0 {
backward -= 1 ;
}
}
true
}
fn main() {
let mut solution : Vec<u32> = Vec::new( ) ;
let mut sum : u32 = 0 ;
let mut current : u32 = 0 ;
while sum < 50 {
current += 1 ;
if is_upside_down( current ) {
solution.push( current ) ;
sum += 1 ;
}
}
let five_hundr : u32 ;
while sum != 500 {
current += 1 ;
if is_upside_down( current ) {
sum += 1 ;
}
}
five_hundr = current ;
let five_thous : u32 ;
while sum != 5000 {
current += 1 ;
if is_upside_down( current ) {
sum += 1 ;
}
}
five_thous = current ;
println!("The first 50 upside-down numbers:") ;
println!("{:?}" , solution ) ;
println!("The five hundredth such number : {}" , five_hundr) ;
println!("The five thousandth such number : {}" , five_thous ) ;
}</syntaxhighlight>
{{out}}
<pre>
The first 50 upside-down numbers:
[5, 19, 28, 37, 46, 55, 64, 73, 82, 91, 159, 258, 357, 456, 555, 654, 753, 852, 951, 1199, 1289, 1379, 1469, 1559, 1649, 1739, 1829, 1919, 2198, 2288, 2378, 2468, 2558, 2648, 2738, 2828, 2918, 3197, 3287, 3377, 3467, 3557, 3647, 3737, 3827, 3917, 4196, 4286, 4376, 4466]
The five hundredth such number : 494616
The five thousandth such number : 56546545
</pre>
=={{header|Wren}}==
{{trans|Python}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
var genUpsideDown = Fiber.new {
| |||