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A228103
Numbers n whose base-10 digits can be split into two parts, q and r, with n = (q-r)^2.
2
100, 121, 6084, 10000, 10201, 82369, 132496, 1000000, 1002001, 1162084, 1201216, 1656369, 1860496, 100000000, 100020001, 123121216, 330621489, 10000000000, 10000200001, 13967221489, 113322449956, 1000000000000, 1000002000001, 1786590449956, 7438023471076, 100000000000000, 100000020000001, 161983503471076, 366292019505049, 553633229065744, 674650026648676, 9553960107298321, 10000000000000000, 10000000200000001
OFFSET
1,1
COMMENTS
q*10^m+r = (q-r)^2; q,m>0; 0<=r<10^m = A228381^2 - Hans Havermann, Aug 21 2013
LINKS
Daniel Joyce, Robert Israel and Lars Blomberg, Can more of these terms be found?
EXAMPLE
100 = (10-0)^2.
121 = (12-1)^2.
6084 = (6-084)^2.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Hans Havermann, Aug 10 2013
STATUS
approved