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A045878 Numbers k such that rotating digits of k^2 left once still yields a square.

%I A045878 #21 Feb 16 2025 08:32:38
%S A045878 1,2,3,12,14,25,108,122,216,310,1222,2028,2527,3042,11802,12222,13704,
%T A045878 24865,25185,26053,30494,122222,208148,247137,312222,1125786,1222222,
%U A045878 1325080,2084388,2551071,3025794,3037736,3126582,10716846,10787208
%N A045878 Numbers k such that rotating digits of k^2 left once still yields a square.
%C A045878 Squares resulting in leading zeros are excluded.
%C A045878 A090843 is a subsequence. - _Chai Wah Wu_, Apr 23 2022
%H A045878 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquareNumber.html">Square Number</a>
%e A045878 11303148^2 = {1}27761154709904 -> 277611547099041{1} = 16661679^2.
%t A045878 rlsQ[n_]:=Module[{idnrl=RotateLeft[IntegerDigits[n^2]]},First[idnrl]>0 && IntegerQ[Sqrt[FromDigits[idnrl]]]]; Select[Range[11000000],rlsQ] (* _Harvey P. Dale_, Nov 03 2013 *)
%o A045878 (Python)
%o A045878 from itertools import count, islice
%o A045878 from sympy.solvers.diophantine.diophantine import diop_DN
%o A045878 def A045878_gen(): # generator of terms
%o A045878     for l in count(0):
%o A045878         l1, l2 = 10**(l+1), 10**l
%o A045878         yield from sorted(set(abs(y) for z in (diop_DN(10,m*(1-l1)) for m in range(10)) for x, y in z if l1 >= x**2 >= l2))
%o A045878 A045878_list = list(islice(A045878_gen(), 30)) # _Chai Wah Wu_, Apr 23 2022
%Y A045878 Cf. A000290, A045877, A035129, A090843.
%K A045878 nonn,base
%O A045878 1,2
%A A045878 _Erich Friedman_
%E A045878 More terms from _Patrick De Geest_, Nov 15 1998