A232422 Integers n such that n^2 becomes another square under the map 8<=>9 (acting on the decimal digits).

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

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