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

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..41.

Rosetta Code, Kaprekar numbers

Eric Weisstein's World of Mathematics, Kaprekar Number

Wikipedia, Kaprekar number

Prog

(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.

Crossrefs

Sequence in context: A022757 A246308 A365145 * A339273 A017617 A246309

Adjacent sequences: A194215 A194216 A194217 * A194219 A194220 A194221

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 19 2011

Status

approved