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A035090 Non-palindromic squares which when written backwards remain square (and still have the same number of digits).

%I A035090 #39 Feb 10 2025 21:30:30
%S A035090 144,169,441,961,1089,9801,10404,10609,12544,12769,14884,40401,44521,
%T A035090 48841,90601,96721,1004004,1006009,1022121,1024144,1026169,1042441,
%U A035090 1044484,1062961,1212201,1214404,1216609,1236544,1238769,1256641
%N A035090 Non-palindromic squares which when written backwards remain square (and still have the same number of digits).
%C A035090 Squares with trailing zeros not included.
%C A035090 Sequence is infinite, since it includes, e.g., 10^(2k) + 4*10^k + 4 for all k. - _Robert Israel_, Sep 20 2015
%H A035090 Robert Israel, <a href="/A035090/b035090.txt">Table of n, a(n) for n = 1..798</a>
%H A035090 Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg2.htm">Palindromic Squares in bases 2 to 17</a>
%H A035090 <a href="/index/Sq#sqrev">Index entry for sequences related to reversing digits of squares</a>
%F A035090 a(n) = A035123(n)^2. - _R. J. Mathar_, Jan 25 2017
%p A035090 rev:= proc(n) local L,i;
%p A035090 L:= convert(n,base,10);
%p A035090 add(L[-i]*10^(i-1),i=1..nops(L))
%p A035090 end proc:
%p A035090 filter:= proc(n) local t;
%p A035090   if n mod 10 = 0 then return false fi;
%p A035090   t:= rev(n);
%p A035090 t <> n and issqr(t)
%p A035090 end proc:
%p A035090 select(filter, [seq(n^2, n=1..10^5)]); # _Robert Israel_, Sep 20 2015
%t A035090 Select[Range[1200]^2,!PalindromeQ[#]&&IntegerLength[#]==IntegerLength[ IntegerReverse[ #]] && IntegerQ[Sqrt[IntegerReverse[#]]]&] (* _Harvey P. Dale_, Jul 19 2023 *)
%Y A035090 Reversing a polytopal number gives a polytopal number:
%Y A035090 cube to cube: A035123, A035124, A035125, A002781;
%Y A035090 square to square: A161902, A035090, A033294, A106323, A106324, A002779;
%Y A035090 square to triangular: A181412, A066702;
%Y A035090 tetrahedral to tetrahedral: A006030;
%Y A035090 triangular to square: A066703, A179889;
%Y A035090 triangular to triangular: A066528, A069673, A003098, A066569.
%Y A035090 Cf. A319388.
%K A035090 nonn,base
%O A035090 1,1
%A A035090 _Patrick De Geest_, Nov 15 1998