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A322835 Non-palindromic numbers n such that n * reverse(n) is a square and n and reverse(n) do not have the same number of digits.

%I A322835 #104 Jan 31 2019 05:15:53
%S A322835 100,200,300,400,500,600,700,800,900,1100,2200,3300,4400,5500,6600,
%T A322835 7700,8800,9900,10000,10100,11100,12100,13100,14100,14400,15100,16100,
%U A322835 16900,17100,18100,19100,20000,20200,21200,22200,23200,24200,25200,26200,27200,28200,28800,29200,30000,30300
%N A322835 Non-palindromic numbers n such that n * reverse(n) is a square and n and reverse(n) do not have the same number of digits.
%C A322835 The terms in this sequence are mostly of the form m * 100^k with k >= 1, but this condition is not sufficient.
%C A322835 A062917 U {this sequence} = A070760, with empty intersection.
%C A322835 There are exactly four families of such integers here: numbers of the forms A002113(j)*100^k, A035090(j)*100^k, A082994(j)*100^k and A323061(j)*10^(2k+1).
%C A322835 All terms are multiples of 10, but they are not necessarily multiples of 100. The first multiple of 10 that is not a multiple of 100 is a(755) = 5449680, and there are only 30 such terms among the first 10000 terms. - _Chai Wah Wu_, Jan 07 2019
%H A322835 Chai Wah Wu, <a href="/A322835/b322835.txt">Table of n, a(n) for n = 1..10000</a>
%e A322835 Example for family 1: 200 * 2 = 400 = 20^2;
%e A322835 Example for family 2: 14400 * 441 = 120^2 * 21^2 = 2520^2;
%e A322835 Example for family 3: 28800 * 882 = (2 * 120^2) * (2 * 21^2) = 5040^2.
%e A322835 Example for family 4: 5449680 * 869445 = 2176740^2. - _Chai Wah Wu_, Jan 07 2019
%t A322835 Select[100 Range@303, And[! PalindromeQ@ #, IntegerQ@ Sqrt[#1 #2], UnsameQ @@ IntegerLength@ {#1, #2}] & @@ {#, IntegerReverse@ #} &] (* _Michael De Vlieger_, Jan 03 2019 *)
%o A322835 (PARI) is(n) = n % 10 == 0 && issquare(n * fromdigits(Vecrev(digits(n)))) \\ _David A. Corneth_, Jan 03 2019
%Y A322835 Cf. A002113, A004086, A035090, A062917, A070760, A082994, A323061.
%K A322835 nonn,base
%O A322835 1,1
%A A322835 _Bernard Schott_, Jan 02 2019