|
%I #15 Jun 17 2022 18:36:55
%S 621,629,6210,6290,43415,44665,62100,62900,113405,113845,434150,
%T 446650,621000,629000,677131,677869,918545,971455,1134050,1138450,
%U 1260718,1264282,1355425,1391825,3373885,3375365,3854525,3867475,4341500,4466500,6210000,6290000,6771310,6778690,9185450,9714550
%N Integers n such that n^2 becomes another square under the map 8<=>9 (acting on the decimal digits).
%C If n is a term then 10n is also a term.
%C n^2 must contain an 8, a 9, or both. - _Harvey P. Dale_, Jun 17 2022
%e 621^2=385641 <=> 395641 = 629^2, so both 621 and 629 are terms.
%e 43415=1884862225 <=>1994962225=44665^2, so both 43415 and 44665 are terms.
%t fQ[n_]:=Block[{id=IntegerDigits@n^2},(MemberQ[id,8]||MemberQ[id,9])&&
%t IntegerQ[Sqrt[FromDigits[id/.{8->9,9->8}]]]]; Reap[Do[If[fQ[n],Sow[n]],{n,10000000}]][[2,1]]
%t Select[Range[10^7],Max[IntegerDigits[#^2]]>7&&IntegerQ[Sqrt[ FromDigits[ IntegerDigits[ #^2]/.{8->9,9->8}]]]&] (* _Harvey P. Dale_, Jun 17 2022 *)
%Y A175789 (primes with similar property).
%K nonn,base
%O 1,1
%A _Zak Seidov_, Nov 23 2013
|
