A035126 - OEIS

%I #24 Sep 08 2022 08:44:52

%S 1,4,9,256,441,961,16641,48841,61009,66564,1127844,2537649,3857296,

%T 4932841,182682256,298840369,342842256,392872041,493772841,787588096,

%U 877996161,10766967696,33255899044,49382172841,74825772849

%N Squares when digits rotated right once remain square.

%C Those resulting in leading zeros excluded.

%H Chai Wah Wu, <a href="/A035126/b035126.txt">Table of n, a(n) for n = 1..1838</a>

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

%F a(n) = A045877(n)^2. - _R. J. Mathar_, Jan 25 2017

%e 2221^2 = 4932841 -> 1493284 = 1222^2. Note that the root behaves accordingly!

%t Select[Range[300000]^2,IntegerQ[Sqrt[FromDigits[RotateRight[ IntegerDigits[ #]]]]]&] (* _Harvey P. Dale_, Mar 22 2015 *)

%o (Magma) [k:k in [m^2:m in [1..10^6]]| IsSquare(Seqint( (Intseq(Floor(k/10)) cat  [ Intseq(k)[1]])))]; // _Marius A. Burtea_, Oct 08 2019

%o (Python)

%o from itertools import count, islice

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

%o def A035126_gen(): # generator of terms

%o     for l in count(0):

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

%o         yield from sorted(set(x**2 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 A035126_list = list(islice(A035126_gen(),30)) # _Chai Wah Wu_, Apr 23 2022

%Y Cf. A045877, A035130.

%K nonn,base

%O 1,2

%A _Patrick De Geest_, Nov 15 1998