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A358705 Zeroless pandigital numbers whose square has each digit 1 to 9 twice.

%I A358705 #24 Dec 01 2022 17:21:03
%S A358705 345918672,351987624,359841267,394675182,429715863,439516278,
%T A358705 487256193,527394816,527498163,528714396,572493816,592681437,
%U A358705 729564183,746318529,749258163,754932681,759142683,759823641,762491835,783942561,784196235,845691372,891357624,914863275,915786423,923165487,928163754,976825431
%N A358705 Zeroless pandigital numbers whose square has each digit 1 to 9 twice.
%e A358705 345918672 is a term since its square 119659727638243584 contains all digits 1..9 twice each.
%p A358705 R:= NULL:
%p A358705 for t in combinat:-permute([$1..9]) do
%p A358705   x:= add(t[i]*10^(i-1),i=1..9);
%p A358705   if sort(convert(x^2,base,10)) = [seq(i$2,i=1..9)] then
%p A358705     R:= R, x
%p A358705   fi
%p A358705 od:
%p A358705 sort([R]); # _Robert Israel_, Nov 27 2022
%o A358705 (Python)
%o A358705 from itertools import permutations as per
%o A358705 a=[]
%o A358705 for n in [int(''.join(d)) for d in per('123456789', 9)]:
%o A358705     if all(str(n**2).count(d) ==2 for d in '123456789'):
%o A358705         a.append(n)
%o A358705 print(a)
%Y A358705 Cf. A050289, A199630.
%K A358705 nonn,base,fini,full
%O A358705 1,1
%A A358705 _Zhining Yang_, Nov 27 2022