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
A247262
Positive squares not ending in 00 that remain squares when prefixed with 100.
Original entry on oeis.org
126609965386962890625, 2251582387232059478759765625, 35195816356873080847263336181640625, 507081064881263080149056017398834228515625, 6906141992927910623080625169910490512847900390625, 90266080419142123943961730174907133914530277252197265625
Offset: 1
126609965386962890625 and 100126609965386962890625 are both squares.
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for(n=1,10^30,if(n^2%100&&issquare(10^(#Str(n^2)+2)+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
A247312
Positive numbers not divisible by 10 whose squares remain squares when prefixed with 100.
Original entry on oeis.org
11252109375, 47450841796875, 187605480615234375, 712096246922607421875, 2627953955633148193359375, 9500846300153588104248046875, 29357159521824837441192448139190673828125, 80932484400013426603726400434970855712890625, 218326368611836548856645001359283924102783203125
Offset: 1
11252109375^2 = 126609965386962890625 and 100126609965386962890625 is square.
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