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A331895 Positive numbers k such that the binary and negabinary representations of k and the negabinary representation of -k are all palindromic.

%I A331895 #10 Jan 31 2020 04:16:25
%S A331895 1,5,7,17,21,31,65,85,127,257,273,325,341,455,511,1025,1105,1285,1365,
%T A331895 1799,2047,4097,4161,4369,4433,5125,5189,5397,5461,7175,7967,8191,
%U A331895 16385,16705,17425,17745,20485,20805,21525,21845,28679,29127,31775,32767,65537,65793
%N A331895 Positive numbers k such that the binary and negabinary representations of k and the negabinary representation of -k are all palindromic.
%C A331895 Numbers of the form 2^(2*m-1) - 1 (A083420) and 2^(2*m) + 1 (A052539) are terms.
%H A331895 Amiram Eldar, <a href="/A331895/b331895.txt">Table of n, a(n) for n = 1..1000</a>
%e A331895 7 is a term since the binary representation of 7, 111, the negabinary representation of 7, 11011, and the negabinary representation of -7, 1001, are all palindromic.
%t A331895 binPalinQ[n_] := PalindromeQ @ IntegerDigits[n, 2]; negabin[n_] := negabin[n] = If[n==0, 0, negabin[Quotient[n-1, -2]]*10 + Mod[n, 2]]; nbPalinQ[n_] := And @@(PalindromeQ @ negabin[#] & /@ {n, -n}); Select[Range[2^16], binPalinQ[#] && nbPalinQ[#] &]
%Y A331895 Intersection of A006995 and A331893.
%Y A331895 Intersection of A331892 and A331894.
%Y A331895 Cf. A039724, A331891.
%K A331895 nonn,base
%O A331895 1,2
%A A331895 _Amiram Eldar_, Jan 30 2020