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A275028 Squares whose digital rotation is also a square.

%I A275028 #51 Apr 10 2024 19:08:41
%S A275028 1,121,196,529,625,961,6889,10201,69169,1002001,1022121,1212201,
%T A275028 5221225,100020001,100220121,109181601,121022001,522808225,602555209,
%U A275028 10000200001,10002200121,10020210201,10201202001,12100220001,62188888129,1000002000001
%N A275028 Squares whose digital rotation is also a square.
%C A275028 From _Jon E. Schoenfield_, Nov 13 2016: (Start)
%C A275028 It is assumed that the rotation changes each digit 6 to a 9 and vice versa, and that the digits 0, 1, 2, 5, and 8 are unchanged by the rotation, as is the case with a seven-segment display in which the digits are formed basically as follows:
%C A275028 .    _       _   _         _    _   _    _    _
%C A275028     | |  |   _|  _|  |_|  |_   |_    |  |_|  |_|
%C A275028     |_|  |  |_   _|    |   _|  |_|   |  |_|   _|
%C A275028 (End)
%C A275028 Sequence is infinite since (10^m+1)^2 for m>0 are terms. Leading zeros after rotation are not allowed, as otherwise 10^m would be terms. All terms start and end with digits 1, 5, 6 or 9. - _Chai Wah Wu_, Apr 09 2024
%H A275028 Chai Wah Wu, <a href="/A275028/b275028.txt">Table of n, a(n) for n = 1..164</a>
%H A275028 Prime Curios, <a href="https://primes.utm.edu/curios/page.php/31.html">31</a>
%e A275028 961 becomes 196 under such a rotation.
%t A275028 Select[Range[10^6]^2, If[Or[IntersectingQ[#, {3, 4, 7}], Last@# == 0], False, IntegerQ@ Sqrt@ FromDigits[Reverse@ # /. {6 -> 9, 9 -> 6}]] &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Nov 14 2016 *)
%o A275028 (Python)
%o A275028 from itertools import count, islice
%o A275028 from sympy.ntheory.primetest import is_square
%o A275028 def A275028_gen(): # generator of terms
%o A275028     r, t = ''.maketrans('69','96'), set('0125689')
%o A275028     for l in count(1):
%o A275028         if l%10:
%o A275028             m = l**2
%o A275028             if set(s:=str(m)) <= t and is_square(int(s[::-1].translate(r))):
%o A275028                 yield m
%o A275028 A275028_list = list(islice(A275028_gen(),10)) # _Chai Wah Wu_, Apr 09 2024
%Y A275028 Cf. A178316.
%K A275028 nonn,base
%O A275028 1,2
%A A275028 _Seiichi Manyama_, Nov 12 2016