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A325149 Squares which can be expressed as the product of a number and its reverse in exactly one way.

%I A325149 #49 Aug 01 2019 04:02:52
%S A325149 0,1,4,9,16,25,36,49,64,81,100,121,400,484,900,1089,1600,1936,2500,
%T A325149 3025,3600,4356,4900,5929,6400,7744,8100,9801,10000,10201,12100,12321,
%U A325149 14641,17161,19881,22801,25921,29241,32761,36481,40000,40804,44944,48400,49284,53824,58564,68644,73984,79524,85264,90000
%N A325149 Squares which can be expressed as the product of a number and its reverse in exactly one way.
%C A325149 The first 47 terms of this sequence (from 0 to 58564) are identical to the first 47 terms of A325148. The square 63504 is not present because it can be expressed in two ways: 63504 = 252 * 252 = 144 * 441.
%C A325149 There are three families of squares in this sequence:
%C A325149 1) Squares of palindromes in A002113\A117281.
%C A325149 2) Squares of non-palindromes which form the sequence A325151.
%C A325149 These squares are a subsequence of A076750.
%C A325149 3) Squares of (m*10^q) with q >= 1 and m palindrome in A002113\A117281.
%D A325149 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition, p. 168.
%H A325149 Chai Wah Wu, <a href="/A325149/b325149.txt">Table of n, a(n) for n = 1..10000</a>
%e A325149 For each family:
%e A325149 1) Square of palindromes: 53824 = 232^2 = 232 * 232.
%e A325149 2) Square of non-palindromes m^2 = k*rev(k) with k and rev(k) which have the same number of digits: 162409 = 403^2 = 169 * 961.
%e A325149 3) Square ends with zeros: 48400 = 220^2 = 2200 * 22.
%Y A325149 Cf. A325148 (at least one way), A083408 (at least two ways), A325150 (exactly two ways), A307019 (exactly three ways).
%Y A325149 Cf. A014186 (squares of palindromes), A076750.
%K A325149 nonn,base
%O A325149 1,3
%A A325149 _Bernard Schott_, Apr 03 2019
%E A325149 a(52) corrected by _Chai Wah Wu_, Apr 11 2019
%E A325149 Definition corrected by _N. J. A. Sloane_, Aug 01 2019