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Numbers k such that rotating digits of k^2 left once still yields a square.
4

%I #20 Apr 24 2022 01:23:02

%S 1,2,3,12,14,25,108,122,216,310,1222,2028,2527,3042,11802,12222,13704,

%T 24865,25185,26053,30494,122222,208148,247137,312222,1125786,1222222,

%U 1325080,2084388,2551071,3025794,3037736,3126582,10716846,10787208

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

%C Squares resulting in leading zeros are excluded.

%C A090843 is a subsequence. - _Chai Wah Wu_, Apr 23 2022

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number</a>

%e 11303148^2 = {1}27761154709904 -> 277611547099041{1} = 16661679^2.

%t 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 (Python)

%o from itertools import count, islice

%o from sympy.solvers.diophantine.diophantine import diop_DN

%o def A045878_gen(): # generator of terms

%o for l in count(0):

%o l1, l2 = 10**(l+1), 10**l

%o 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_list = list(islice(A045878_gen(), 30)) # _Chai Wah Wu_, Apr 23 2022

%Y Cf. A000290, A045877, A035129, A090843.

%K nonn,base

%O 1,2

%A _Erich Friedman_

%E More terms from _Patrick De Geest_, Nov 15 1998