First perfect square in base n with n unique digits: Difference between revisions
First perfect square in base n with n unique digits (view source)
Revision as of 11:16, 17 April 2024
, 1 month ago→{{header|EasyLang}}
(Added Quackery.) |
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</pre>
=={{header|EasyLang}}==
{{trans|Nim}}
<syntaxhighlight>
alpha$ = "0123456789AB"
func$ itoa n b .
if n > 0
return itoa (n div b) b & substr alpha$ (n mod b + 1) 1
.
.
func unique s$ .
len dig[] 12
for c$ in strchars s$
ind = strpos alpha$ c$
dig[ind] = 1
.
for v in dig[]
cnt += v
.
return cnt
.
proc find b . .
n = floor pow b ((b - 1) div 2)
repeat
sq = n * n
sq$ = itoa sq b
until len sq$ >= b and unique sq$ = b
n += 1
.
n$ = itoa n b
print "Base " & b & ": " & n$ & "² = " & sq$
.
for base = 2 to 12
find base
.
</syntaxhighlight>
{{out}}
<pre>
Base 2: 10² = 100
Base 3: 22² = 2101
Base 4: 33² = 3201
Base 5: 243² = 132304
Base 6: 523² = 452013
Base 7: 1431² = 2450361
Base 8: 3344² = 13675420
Base 9: 11642² = 136802574
Base 10: 32043² = 1026753849
Base 11: 111453² = 1240A536789
Base 12: 3966B9² = 124A7B538609
</pre>
=={{header|F_Sharp|F#}}==
Line 807 ⟶ 857:
16 404A9D9B² = 1025648CFEA37BD9
</pre>
=={{header|FreeBASIC}}==
{{trans|XPLo}}
<syntaxhighlight lang="vbnet">#define floor(x) ((x*2.0-0.5) Shr 1)
Dim Shared As Double n, base_ = 2. ' Base is a reserved word on FB
Sub NumOut(n As Double) 'Display n in the specified base
Dim As Integer remainder = Fix(n Mod base_)
n = floor(n / base_)
If n <> 0. Then NumOut(n)
Print Chr(remainder + Iif(remainder <= 9, Asc("0"), Asc("A")-10));
End Sub
Function isPandigital(n As Double) As Boolean
Dim As Integer used, remainder
used = 0
While n <> 0.
remainder = Fix(n Mod base_)
n = floor(n / base_)
used Or= 1 Shl remainder
Wend
Return used = (1 Shl Fix(base_)) - 1
End Function
Do
n = floor(Sqr(base_ ^ (base_-1.)))
Do
If isPandigital(n*n) Then
Print Using "Base ##: "; base_;
NumOut(n)
Print "^2 = ";
NumOut(n*n)
Print
Exit Do
End If
n += 1.
Loop
base_ += 1.
Loop Until base_ > 14.
Sleep</syntaxhighlight>
{{out}}
<pre>Base 2: 10^2 = 100
Base 3: 22^2 = 2101
Base 4: 33^2 = 3201
Base 5: 243^2 = 132304
Base 6: 523^2 = 452013
Base 7: 1431^2 = 2450361
Base 8: 3344^2 = 13675420
Base 9: 11642^2 = 136802574
Base 10: 32043^2 = 1026753849
Base 11: 111453^2 = 1240A536789
Base 12: 3966B9^2 = 124A7B538609
Base 13: 3828943^2 = 10254773CA86B9
Base 14: 3A9DB7C^2 = 10269B8C57D3A4</pre>
=={{header|Go}}==
Line 3,654 ⟶ 3,760:
=={{header|Quackery}}==
<code>from</code>, <code>index</code>, and <code>end</code> are defined at [[Loops/Increment loop index within loop body#Quackery]].
<syntaxhighlight lang="Quackery"> [ dup 1
Line 3,681 ⟶ 3,789:
pandigital if
[ index end ] ]
say "Base " decimal echo
base release
say ": " dup echo
cr base release ]</syntaxhighlight>
{{out}}
<pre>Base 2: 10^
Base 3: 22^2 = 2101
Base 4: 33^2 = 3201
Line 4,006 ⟶ 4,111:
in base: 10 root: 32043 square: 1026753849 perfect square: 1026753849
done...
</pre>
=={{header|RPL}}==
{{works with|HP|49}}
≪ → base
≪ { } base + 0 CON SWAP
'''WHILE''' DUP '''REPEAT'''
base IDIV2
ROT SWAP 1 + DUP PUT SWAP
'''END'''
DROP OBJ→ 1 GET →LIST ΠLIST
≫ ≫ '<span style="color:blue">PANB?</span>' STO <span style="color:grey">@ ''( number base → boolean )''</span>
≪ → base
≪ ""
'''WHILE''' OVER '''REPEAT'''
SWAP base IDIV2
"0123456789ABCDEF" SWAP 1 + DUP SUB
ROT +
'''END'''
SWAP DROP
≫ ≫ '<span style="color:blue">→B</span>' STO <span style="color:grey">@ ''( number_10 base → "number_base" )''</span>
≪ → base
≪ 0
1 base 1 - '''FOR''' j <span style="color:grey">@ this loop generates the smallest pandigital number for the base</span>
base
'''IF''' j 2 == '''THEN''' SQ '''END'''
* j +
'''NEXT'''
√ IP
'''WHILE''' DUP SQ base <span style="color:blue">PANB?</span> NOT '''REPEAT''' 1 + '''END'''
base ": " +
OVER base <span style="color:blue">→B</span> + "² = " +
SWAP SQ base <span style="color:blue">→B</span> +
≫ ≫ ‘<span style="color:blue">SQPAN</span>’ STO <span style="color:grey">@ ''( → "base: n² = pandigital" )''</span>
≪ { }
2 15 '''FOR''' b
base <span style="color:blue">SQPAN</span> + '''NEXT'''
≫ ‘<span style="color:blue">TASK</span>’ STO
The above code can be run on a HP-48G if <code>IDIV2</code> is implemented such as : <code>≪ MOD LASTARG / IP SWAP ≫</code>
{{out}}
<pre>
1: { "2: 10² = 100" "3: 22² = 2101" "4: 33² = 3201" "5: 243² = 132304" "6: 523² = 452013" "7: 1431² = 2450361"
"8: 3344² = 13675420" "9: 11642² = 136802574" "10: 32043² = 1026753849" "11: 111453² = 1240A536789" "12: 3966B9² = 124A7B538609" "13: 3828943² = 10254773CA86B9" "14: 3A9DB7C² = 10269B8C57D3A4" "15: 1012B857² = 102597BACE836D4" }
</pre>
Line 4,069 ⟶ 4,220:
</pre>
=={{header|Uiua}}==
No integer arithmetic in Uiua, so it's a bit slow...
<syntaxhighlight lang="Uiua">
BaseN ← setinv(↘2⍢(⊂⊂:⊙(⊃(↙1)(↘2))⊂⊃(⌊÷)◿°⊟↙2.)(>0 ⊢↘1)⊟|/+×ⁿ:⊙(⇌⇡⧻.))
IsPan ← =⧻◴: # IsPan 3 [0 1 2]
# Smallest pan number for given base
# = [1 0 2 3 4...] in base n
MinPanBase ← °BaseN ⟜(↙:⊂[1 0]↘2⇡+1.)
MinPanSqrBase ← ⊙◌⍢(+1)(¬IsPan :BaseN ,×.) ⌊√MinPanBase.
ShowMinPan ← (
≡(
&pf "\t" &pf . &pf "Base "
MinPanSqrBase .
&p BaseN : &pf "\t" &pf. × &pf "\t" &pf. .
)
)
⍜now (ShowMinPan ↘2⇡13)
</syntaxhighlight>
{{out}}
<pre>
stdout:
Base 2 2 4 [1 0 0]
Base 3 8 64 [2 1 0 1]
Base 4 15 225 [3 2 0 1]
Base 5 73 5329 [1 3 2 3 0 4]
Base 6 195 38025 [4 5 2 0 1 3]
Base 7 561 314721 [2 4 5 0 3 6 1]
Base 8 1764 3111696 [1 3 6 7 5 4 2 0]
Base 9 7814 61058596 [1 3 6 8 0 2 5 7 4]
Base 10 32043 1026753849 [1 0 2 6 7 5 3 8 4 9]
Base 11 177565 31529329225 [1 2 4 0 10 5 3 6 7 8 9]
Base 12 944493 892067027049 [1 2 4 10 7 11 5 3 8 6 0 9]
17.243999999999915 [ooof]
</pre>
=={{header|Visual Basic .NET}}==
{{libheader|System.Numerics}}
Line 4,183 ⟶ 4,371:
{{libheader|Wren-fmt}}
Base 21 is as far as we can reasonably fly here though (unsurprisingly) base 20 takes a long time.
<syntaxhighlight lang="
import "./math" for Nums
import "./fmt" for Conv, Fmt
var maxBase = 21
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