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%I #26 Aug 28 2014 10:32:42
%S 0,1,2,3,13,113,1113,11113,1011113,101011113,1101111211,110101111211,
%T 100110101111211,10101010101101122,1011111111100000013,
%U 1010111111111000000022,111000010111000111111111,1010110111101110100000011111,1111111110010101100001100000102
%N Smallest skinny number (A061909) with digit sum n.
%C The smallest m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.
%C There are infinitely many natural numbers m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.
%H Hiroaki Yamanouchi, <a href="/A224792/b224792.txt">Table of n, a(n) for n = 0..19</a>
%F a(n) > 2/9 * 10^(n/2) for n > 4. - _Charles R Greathouse IV_, Apr 18 2013
%t DS[n_] := Total[IntegerDigits[n]]; nn = 10; t = Table[0, {nn}]; n = 0; found = 0; While[n++; r = FromDigits[IntegerDigits[n, 4]]; found < nn, If[DS[r]^2 == DS[r^2] && DS[r] <= nn && t[[DS[r]]] == 0, t[[DS[r]]] = r; found++; Print[r]]]; Join[{0}, t] (* _T. D. Noe_, Apr 18 2013 *)
%Y Cf. A061909.
%K nonn,base
%O 0,3
%A _Reiner Moewald_, Apr 18 2013
%E a(10) corrected and a(11) added by _T. D. Noe_, Apr 18 2013
%E a(12)-a(13) from _Donovan Johnson_, Apr 19 2013
%E a(14) from _Donovan Johnson_, Apr 24 2013
%E a(15)-a(18) from _Hiroaki Yamanouchi_, Aug 28 2014