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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.

%I A248353 #9 Feb 16 2025 08:33:23
%S A248353 1,9,10,45,55,99,100,297,703,999,1000,2223,2728,4879,4950,5050,5292,
%T A248353 7272,7777,9999,10000,17344,22222,38962,77778,82656,95121,99999,
%U A248353 100000,142857,148149,181819,187110,208495,318682,329967,351352,356643,390313,461539
%N 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.
%C A248353 Powers of 10 were excluded in Kaprekar's original definition (A006886), see also A045913.
%H A248353 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KaprekarNumber.html">Kaprekar Number</a>
%H A248353 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kaprekar_number">Kaprekar number</a>
%F A248353 a(n) = sqrt(A102766(n)).
%o A248353 (Haskell)
%o A248353 a248353 n = a248353_list !! (n-1)
%o A248353 a248353_list = filter k [1..] where
%o A248353    k x = elem x $ map (uncurry (+)) $
%o A248353          takeWhile ((> 0) . fst) $ map (divMod (x ^ 2)) a011557_list
%Y A248353 Cf. A006886 (subsequence), A045913, A053816, A011557, A102766.
%K A248353 nonn
%O A248353 1,2
%A A248353 _Reinhard Zumkeller_, Oct 05 2014