

A232422


Integers n such that n^2 becomes another square under the map 8<=>9 (acting on the decimal digits).


0



621, 629, 6210, 6290, 43415, 44665, 62100, 62900, 113405, 113845, 434150, 446650, 621000, 629000, 677131, 677869, 918545, 971455, 1134050, 1138450, 1260718, 1264282, 1355425, 1391825, 3373885, 3375365, 3854525, 3867475, 4341500, 4466500, 6210000, 6290000, 6771310, 6778690, 9185450, 9714550
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OFFSET

1,1


COMMENTS

If n is a term then 10n is also a term.
n^2 must contain an 8, a 9, or both.  Harvey P. Dale, Jun 17 2022


LINKS

Table of n, a(n) for n=1..36.


EXAMPLE

621^2=385641 <=> 395641 = 629^2, so both 621 and 629 are terms.
43415=1884862225 <=>1994962225=44665^2, so both 43415 and 44665 are terms.


MATHEMATICA

fQ[n_]:=Block[{id=IntegerDigits@n^2}, (MemberQ[id, 8]MemberQ[id, 9])&&
IntegerQ[Sqrt[FromDigits[id/.{8>9, 9>8}]]]]; Reap[Do[If[fQ[n], Sow[n]], {n, 10000000}]][[2, 1]]
Select[Range[10^7], Max[IntegerDigits[#^2]]>7&&IntegerQ[Sqrt[ FromDigits[ IntegerDigits[ #^2]/.{8>9, 9>8}]]]&] (* Harvey P. Dale, Jun 17 2022 *)


CROSSREFS

A175789 (primes with similar property).
Sequence in context: A202239 A010031 A252527 * A335767 A189119 A203086
Adjacent sequences: A232419 A232420 A232421 * A232423 A232424 A232425


KEYWORD

nonn,base


AUTHOR

Zak Seidov, Nov 23 2013


STATUS

approved



