A198035 Numbers n such that n^2 is a concatenation of two nonzero squares with no trailing zeros in n.

7, 13, 19, 35, 38, 41, 57, 65, 125, 205, 223, 253, 285, 305, 475, 487, 721, 905, 975, 985, 1012, 1201, 1265, 1301, 1442, 1518, 1771, 2024, 2163, 2225, 2277, 2402, 2435, 3075, 3125, 3925, 4901, 6013, 7045, 7969, 8225, 8855, 9607, 9625, 9805, 10815, 11125, 11385, 12025

Offset: 1

Author

Zak Seidov, Oct 20 2011

Keywords

• nonn
• base

Comments

Primitive solutions of A048375 (whose numbers can have trailing zeros).

Examples

			a(150)=1002445 and 1002445^2=1004895978025=100489_5978025, x^2=317^2=100489, y^2=2445^2=5978025.
		

Links

• Zak Seidov, 150 values for n,a,b

Crossrefs

Cf. A048375.

Programs

Mathematica

Reap[Do[r=0; If[Mod[n,10]>0, Do[mo=PowerMod[n,2,10^k]; If[mo>10^(k-1)-1 && IntegerQ[Sqrt[mo]] && IntegerQ[Sqrt[qu=Quotient[n^2,10^k]]], r=1; Break[]], {k,Log[10,n^2]}]; If[r>0,Sow[n]; Print[{n,Sqrt[qu],Sqrt@mo}]]], {n,7,10^6}]][[2,1]] (* Zak Seidov, Oct 20 2011 *)