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A198035 Numbers n such that n^2 is a concatenation of two nonzero squares with no trailing zeros in n. 1

%I #19 Oct 30 2018 10:31:02

%S 7,13,19,35,38,41,57,65,125,205,223,253,285,305,475,487,721,905,975,

%T 985,1012,1201,1265,1301,1442,1518,1771,2024,2163,2225,2277,2402,2435,

%U 3075,3125,3925,4901,6013,7045,7969,8225,8855,9607,9625,9805,10815,11125,11385,12025

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

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

%H Zak Seidov, <a href="/A198035/a198035.txt">150 values for n,a,b</a>

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

%t 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 *)

%Y Cf. A048375.

%K nonn,base

%O 1,1

%A _Zak Seidov_, Oct 20 2011

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)