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A356648 Numbers whose square is of the form k + reversal of digits of k, for some k.

%I A356648 #56 Mar 15 2023 10:55:56
%S A356648 2,4,11,22,25,33,101,121,141,202,222,264,303,307,451,836,1001,1111,
%T A356648 1221,1232,2002,2068,2112,2222,2305,2515,2626,2636,2776,3003,3958,
%U A356648 3972,4015,4081,7975,8184,9757,10001,10201,10401,11011,11121,11211,12012,12021,12221,13046,16581,20002
%N A356648 Numbers whose square is of the form k + reversal of digits of k, for some k.
%C A356648 Square roots of the squares in A067030.
%H A356648 Hugo Pfoertner, <a href="/A356648/b356648.txt">Table of n, a(n) for n = 1..2253</a>, using results from participants Sebastian and l4m2 at the Code Golf challenge.
%H A356648 Nicolay Avilov, <a href="https://www.diofant.ru/problem/4216/">Problem 2422. Mirror numbers</a> (in Russian).
%H A356648 Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/questions/256224/radd-decomposition-of-an-integer">RADD decomposition of an integer</a>, coding challenge started Jan 01 2023.
%F A356648 a(n) = sqrt(A358880(n)). - _Michel Marcus_, Dec 25 2022
%e A356648 4 is a term since 4^2 = 16 = 8 + 8;
%e A356648 11 is a term since 11^2 = 121 = 29 + 92 is sum of k=29 and its reversal 92;
%e A356648 22 is a term since 22^2 = 484 = 143 + 341;
%e A356648 10201 is a term since 10201^2 = 104060401 = 100030400 + 4030001.
%o A356648 (PARI) L=vectorsmall(100000);
%o A356648 \\ Takes a few minutes of CPU time
%o A356648 for (k=1, 2*10^8, my(d=digits(k), r=fromdigits(Vecrev(d)), s); if (issquare(k+r, &s), L[s]=1));
%o A356648 for (k=1, 21000, if(L[k], print1(k,", "))) \\ _Hugo Pfoertner_, Dec 13 2022
%o A356648 (C++, Haskell) See Code Golf link.
%Y A356648 Cf. A056964, A061230, A067030, A358880, A358984.
%K A356648 nonn,base
%O A356648 1,1
%A A356648 _Nicolay Avilov_, data a(10)-a(37) from Oleg Sorokin, Dec 10 2022
%E A356648 a(38) and beyond from _Hugo Pfoertner_, Dec 12 2022