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

Offset: 1

Author

Hans Havermann, Aug 10 2013

Keywords

• nonn
• base

Comments

q*10^m+r = (q-r)^2 = A228381^2; q,m>0; 0<=r<10^m. - Hans Havermann, Aug 21 2013

Examples

			100 = (10-0)^2.
121 = (12-1)^2.
6084 = (6-084)^2.
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..1016
• Daniel Joyce, Robert Israel and Lars Blomberg, Can more of these terms be found? [broken link?]
• J. B. Wood, Quick Solution to Puzzle?

Crossrefs

Cf. A102766, A118936, A228381.

Programs

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 *)