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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)
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Base 28: 58a3ckp3n4cqd7² = 1023456cgjbirqedhp98kmoan7fl in 911.059s
</pre>
=={{header|Haskell}}==
{{trans|F#}}
<lang haskell>import Control.Monad (guard)
import Data.List (find, unfoldr)
import Data.Char (intToDigit)
import qualified Data.Set as Set
import Text.Printf (printf)
digits :: Integral a => a -> a -> [a]
digits b = unfoldr (\d -> guard (d /= 0) >> pure (d `mod` b, d `div` b))
sequenceForBaseN :: Integral a => a -> [a]
sequenceForBaseN
b = unfoldr (\(v, n) -> Just (v, (v + n, n + 2))) (i ^ 2, i * 2 + 1)
where
i = succ (round $ sqrt (realToFrac (b ^ pred b)))
searchSequence :: Integral a => a -> Maybe a
searchSequence
b = find (\x -> Set.fromList (digits b x) == digitsSet) (sequenceForBaseN b)
where
digitsSet = Set.fromList [0 .. pred b]
display :: Integer -> Integer -> String
display b n = map (intToDigit . fromIntegral) $ reverse $ digits b n
main :: IO ()
main = mapM_
(\b -> case searchSequence b of
Just n -> printf
"Base %2d: %8s² -> %16s\n"
b
(display b (squareRootValue n))
(display b n)
Nothing -> pure ())
[2 .. 16]
where
squareRootValue = round . sqrt . realToFrac</lang>
{{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
Base 13: 3828943² -> 10254773ca86b9
Base 14: 3a9db7c² -> 10269b8c57d3a4
Base 15: 1012b857² -> 102597bace836d4
Base 16: 404a9d9b² -> 1025648cfea37bd9</pre>
=={{header|J}}==
<lang>
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