A194218 Left part of the square of the n-th Kaprekar number.

1, 8, 20, 30, 98, 88, 494, 998, 494, 744, 238, 2450, 2550, 28, 5288, 6048, 9998, 3008, 4938, 1518, 60494, 68320, 90480, 99998, 20408, 21948, 33058, 35010, 43470, 101558, 108878, 123448, 127194, 152344, 213018, 217930, 249500, 250500, 284270, 289940, 371718

Offset: 1

Author

Reinhard Zumkeller, Aug 19 2011

Keywords

• nonn
• base

Comments

a(n) + A194219(n) = A006886(n) and

concatenation of a(n) and A194219(n) = A006886(n)^2.

Links

• Rosetta Code, Kaprekar numbers
• Eric Weisstein's World of Mathematics, Kaprekar Number
• Wikipedia, Kaprekar number

Programs

Haskell

import Data.List (find)
import Data.Maybe (mapMaybe)
a194218 n = a194218_list !! (n-1)
a194218_list = map fst kaprekarPairs
a194219 n = a194219_list !! (n-1)
a194219_list = map snd kaprekarPairs
a006886 n = a006886_list !! (n-1)
a006886_list = map (uncurry (+)) kaprekarPairs
kaprekarPairs = (1,0) : (mapMaybe (\n -> kSplit n $ splits (n^2)) [1..])
   where kSplit x = find (\(left, right) -> left + right == x)
         splits q = no0 . map (divMod q) $ iterate (10 *) 10
         no0 = takeWhile ((> 0) . fst) . filter ((> 0) . snd)
-- Cf. Rosetta link.