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A234472 Numbers that when raised to the fourth power and written backwards give squares.

%I A234472 #38 Nov 19 2022 00:53:49
%S A234472 0,1,10,11,100,101,110,1000,1001,1010,1100,10000,10001,10010,10100,
%T A234472 11000,100000,100001,100010,100100,101000,110000,1000000,1000001,
%U A234472 1000010,1000100,1001000,1010000,1100000,10000000,10000001,10000010,10000100,10001000,10010000
%N A234472 Numbers that when raised to the fourth power and written backwards give squares.
%C A234472 It seems that the numbers contain only the digits 0 and 1, and that the reversed fourth power and the square root of the reversed fourth power are both palindromes.
%C A234472 If the above comment is correct, and also if (as it appears) no more than two ones are among the digits of any term, this Mathematica program quickly generates the terms of the sequence: Flatten[Table[Select[ FromDigits/@Permutations[PadRight[PadRight[{},k,1],8,0]],IntegerQ[ Sqrt[ IntegerReverse[#^4]]]&],{k,0,2}]]//Sort - _Harvey P. Dale_, May 05 2020
%e A234472 101 is in the sequence because 101^4 = 104060401 and 104060401 = 10201^2.
%e A234472 110 is in the sequence because 110^4 = 146410000 and 14641 = 121^2.
%t A234472 Select[Range[0,10^7],IntegerQ[Sqrt[IntegerReverse[#^4]]]&] (* _Harvey P. Dale_, May 05 2020 *)
%o A234472 (PARI) revint(n) = m=n%10; n\=10; while(n>0, m=m*10+n%10; n\=10); m
%o A234472 s=[]; for(i=0, 1000000, if(issquare(revint(i^4)), s=concat(s, i))); s
%o A234472 (Magma) [n: n in [0..10^7] | IsSquare(Seqint(Reverse(Intseq(n^4))))]; // _Bruno Berselli_, Dec 27 2013
%o A234472 (Python)
%o A234472 from itertools import count, islice
%o A234472 from sympy import integer_nthroot
%o A234472 def A234472_gen(startvalue=0): # generator of terms >= startvalue
%o A234472     return filter(lambda n:integer_nthroot(int(str(n**4)[::-1]),2)[1], count(max(startvalue,0)))
%o A234472 A234472_list = list(islice(A234472_gen(),10)) # _Chai Wah Wu_, Nov 18 2022
%Y A234472 Cf. A102859, A043681.
%K A234472 nonn,base,nice
%O A234472 1,3
%A A234472 _Colin Barker_, Dec 26 2013