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%I #31 Jun 22 2018 04:42:47
%S 12,13,21,31,102,103,112,113,122,201,211,221,301,311,1002,1003,1011,
%T 1012,1013,1021,1022,1031,1101,1102,1103,1112,1113,1121,1122,1201,
%U 1202,1211,1212,1301,2001,2011,2012,2021,2022,2101,2102,2111,2121,2201,2202,2211,3001,3011,3101,3111
%N Numbers n not a multiple of 10 such that reverse(n^2) = reverse(n)^2, but reverse(n) is different from n.
%C This sequence is similar to A035123 but excludes integers such as 33 or 99 or 3168, because they don't meet the commutativity criterion reverse(n^2) = (reverse(n))^2.
%C Compare for instance:
%C {reverse(3168^2), reverse(3168)^2} -> {42263001, 74183769}
%C with:
%C {reverse(3111^2), reverse(3111)^2} -> {1238769, 1238769}
%C Terms can be matched by pairs:
%C {{12, 21}, {13, 31}, {102, 201}, {103, 301}, {112, 211}, {113, 311}, {122, 221}, {1002, 2001}, {1003, 3001}, {1011, 1101}, {1012, 2101}, {1013, 3101}, {1021, 1201}, {1022, 2201}, {1031, 1301}, {1102, 2011}, {1103, 3011}, {1112, 2111}, {1113, 3111}, {1121, 1211}, {1122, 2211}, {1202, 2021}, {1212, 2121}, {2012, 2102}, {2022, 2202},...}
%H Giovanni Resta, <a href="/A140212/b140212.txt">Table of n, a(n) for n = 1..10000</a> (first 300 terms from Vincenzo Librandi)
%F a(n)^2 = A064021(n). - _Giovanni Resta_, Jun 22 2018
%e 113 belongs to the sequence because sqrt(reverse(113^2)) = 311, which is 113 written backwards, whereas 99 does not: sqrt(reverse(99^2)) = 33.
%t r[n_] := FromDigits[Reverse[IntegerDigits[n]]];
%t Cases[Range[10000], n_ /; Mod[n, 10] != 0 && r[n^2] != n^2 && r[n^2] == r[n]^2 ]
%Y Cf. A064021. Subsequence of A035123.
%K nonn,base
%O 1,1
%A _Jean-François Alcover_, Mar 08 2011
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