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Positive numbers k such that both k and -k are a palindromes in negabinary representation.
2

%I #10 Jan 31 2020 04:16:00

%S 1,5,7,17,21,31,57,65,85,127,155,217,257,273,325,341,455,511,635,857,

%T 889,993,1025,1105,1253,1285,1365,1799,2047,2159,2555,2667,3417,3577,

%U 3641,3937,4097,4161,4369,4433,4965,5125,5189,5397,5461,6951,7175,7967,8191

%N Positive numbers k such that both k and -k are a palindromes in negabinary representation.

%C Numbers of the form 2^(2*m-1) - 1 (A083420) and 2^(2*m) + 1 (A052539) are terms.

%H Amiram Eldar, <a href="/A331893/b331893.txt">Table of n, a(n) for n = 1..10000</a>

%e 5 is a term since the negabinary representation of 5, 101, and the negabinary representation of -5, 1111, are both palindromic.

%t 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[2^13], nbPalinQ]

%Y Intersection of A331891 and A331892.

%Y Cf. A005352, A039724, A212529.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Jan 30 2020