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

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?

J. B. Wood, Quick Solution to Puzzle?

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

Cf. A102766, A118936, A228381.

Sequence in context: A071987 A365820 A095633 * A331543 A063009 A066139

Adjacent sequences: A228100 A228101 A228102 * A228104 A228105 A228106

Keyword

nonn,base

Author

Hans Havermann, Aug 10 2013

Status

approved