A248353 Kaprekar numbers, allowing powers of 10: n such that n=q+r and n^2=q*10^m+r, for some m >= 1, q>=0 and 0<=r<10^m.

1, 9, 10, 45, 55, 99, 100, 297, 703, 999, 1000, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 10000, 17344, 22222, 38962, 77778, 82656, 95121, 99999, 100000, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539

Offset: 1

Author

Reinhard Zumkeller, Oct 05 2014

Keywords

• nonn

Comments

Powers of 10 were excluded in Kaprekar's original definition (A006886), see also A045913.

Links

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

Crossrefs

Cf. A006886 (subsequence), A045913, A053816, A011557, A102766.

Programs

Haskell

a248353 n = a248353_list !! (n-1)
a248353_list = filter k [1..] where
   k x = elem x $ map (uncurry (+)) $
         takeWhile ((> 0) . fst) $ map (divMod (x ^ 2)) a011557_list

Formula

a(n) = sqrt(A102766(n)).