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A228103 Numbers k whose base-10 digits can be split into two parts, q and r, with k = (q-r)^2.

%I A228103 #31 Jan 12 2025 10:15:57
%S A228103 100,121,6084,10000,10201,82369,132496,1000000,1002001,1162084,
%T A228103 1201216,1656369,1860496,100000000,100020001,123121216,330621489,
%U A228103 10000000000,10000200001,13967221489,113322449956,1000000000000,1000002000001,1786590449956,7438023471076
%N A228103 Numbers k whose base-10 digits can be split into two parts, q and r, with k = (q-r)^2.
%C A228103 q*10^m+r = (q-r)^2 = A228381^2; q,m>0; 0<=r<10^m. - _Hans Havermann_, Aug 21 2013
%H A228103 Hans Havermann, <a href="/A228103/b228103.txt">Table of n, a(n) for n = 1..1016</a>
%H A228103 Daniel Joyce, Robert Israel and Lars Blomberg, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-August/011546.html">Can more of these terms be found?</a> [broken link?]
%H A228103 J. B. Wood, <a href="http://mathforum.org/kb/message.jspa?messageID=9188302">Quick Solution to Puzzle?</a>
%e A228103 100 = (10-0)^2.
%e A228103 121 = (12-1)^2.
%e A228103 6084 = (6-084)^2.
%t A228103 k=3; While[k<10^8, k++; s=k^2; d=IntegerDigits[s]; l=Length[d]; Do[a=FromDigits[Take[d,{1,i}]]; b=FromDigits[Take[d,{i+1,l}]]; If[k==Abs[a-b], w=ToString[s]; Print[StringTake[w,{1,i}], "'", StringTake[w,{i+1,l}]]], {i,l-1}]] (* _Hans Havermann_, Aug 10 2013, Aug 20 2013 *)
%Y A228103 Cf. A102766, A118936, A228381.
%K A228103 nonn,base
%O A228103 1,1
%A A228103 _Hans Havermann_, Aug 10 2013