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100055742..90625^2 = ...1100055742..90625
:The three zeros in the first line make it a zero-fill candidate for three rounds, after which the second line will either "take over the mantle" in the list of potential candidates, or there won't be anything that does. Or it might be more accurate to say it ''only'' becomes a candidate in three rounds time?
:From my experiments so far I... suspectOh, theffs, numberoff ofcourse, candidateshow atdid eachI iterationnot settlesspot into''that''? It is just a simple5-chain patternand a 6-chain, atwith leastthe it1-chain doesdying notinstantly. seemThere towill growonly much,ever be and always will be either one or two n-digit steady square numbers ending in fact5 or 6 or both, maybe with the odd skip when both leap-frog. ''DOH.'' I will however leave it mayup justto someone else to come up with a proof that there will ''always'' be twoa candidatessingle occasionallyprefix hoppingdigit that will work, overfor each otherchain. --[[User:Petelomax|Pete Lomax]] ([[User talk:Petelomax|talk]]) 0102:3805, 24 December 2021 (UTC)
::Oh, ffs, off course, how did I not spot ''that''? It is just a 5-chain and a 6-chain, with the 1-chain dying instantly. There will only ever be and always will be either one or two n-digit steady square numbers ending in 5 or 6 or both, maybe with the odd skip when both leap-frog. ''DOH.'' I will however leave it up to someone else to come up with a proof that there will ''always'' be a single prefix digit that will work, for each chain. --[[User:Petelomax|Pete Lomax]] ([[User talk:Petelomax|talk]]) 02:05, 24 December 2021 (UTC)
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