A247261
Positive squares not ending in 00 that remain squares when prefixed with 10.
Original entry on oeis.org
5625, 50625, 62187890625, 453097265625, 684420119384765625, 4030118984619140625, 7501588188366851806640625, 35596572549171295166015625, 81913198262420037174224853515625, 311932283242100929355621337890625, 891378408151941675529539585113525390625
Offset: 1
5625 and 105625 are both squares.
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for(n=1,10^7,if(n^2%100&&issquare(10^(#Str(n^2)+1)+n^2),print1(n^2,", "))) \\ Derek Orr, Sep 13 2014
A247263
Positive numbers not divisible by 10 whose squares remain squares when prefixed with 1000.
Original entry on oeis.org
375, 2371875, 6816208478590683385931482169914619837072677910327911376953125, 140221743281593822163509288486586064542459780568606220185756683349609375, 818488127823449514709977488133381451695186814276894438080489635467529296875
Offset: 1
375^2 = 140625 and 1000140625 is square.
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for(n=1,10^20,if(n^2%100&&issquare(10^(#Str(n^2)+3)+n^2),print1(n^2,", "))) \\ Derek Orr, Sep 13 2014
A247264
Smallest positive number not divisible by 10 whose square remains a square when prefixed with 10^n.
Original entry on oeis.org
15, 75, 11252109375, 375, 9694963627295445503856592180983186990852118469774723052978515625, 6841439843263141047421876154427540653587129781953990459442138671875
Offset: 0
a(0) = 15 since 15^2 = 225 and 1225 is square and 15 is the smallest number not ending in 0 with this property. a(3) = 375 since 375^2 = 140625 and 1000140625 is square and 375 is the smallest number not ending in 0 with this property.
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a(n)=k=1;while(k^2%100==0||!issquare(10^(#Str(k^2)+n)+k^2),k++);k^2
n=0;while(n<10,print1(a(n),", ");n++) \\ Derek Orr, Sep 13 2014
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