A331895 Positive numbers k such that the binary and negabinary representations of k and the negabinary representation of -k are all palindromic.
1, 5, 7, 17, 21, 31, 65, 85, 127, 257, 273, 325, 341, 455, 511, 1025, 1105, 1285, 1365, 1799, 2047, 4097, 4161, 4369, 4433, 5125, 5189, 5397, 5461, 7175, 7967, 8191, 16385, 16705, 17425, 17745, 20485, 20805, 21525, 21845, 28679, 29127, 31775, 32767, 65537, 65793
Offset: 1
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Mathematica
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[#] &]
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