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A198035
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Numbers n such that n^2 is a concatenation of two nonzero squares with no trailing zeros in n.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Primitive solutions of A048375 (whose numbers can have trailing zeros).
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LINKS
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Table of n, a(n) for n=1..49.
Zak Seidov, 150 values for n,a,b
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EXAMPLE
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a(150)=1002445 and 1002445^2=1004895978025=100489_5978025, x^2=317^2=100489, y^2=2445^2=5978025.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A048375.
Sequence in context: A265629 A283191 A048375 * A208720 A208776 A108295
Adjacent sequences: A198032 A198033 A198034 * A198036 A198037 A198038
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KEYWORD
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nonn,base
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AUTHOR
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Zak Seidov, Oct 20 2011
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STATUS
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approved
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