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

1,2

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

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.

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[#] &]

Crossrefs

Intersection of A006995 and A331893.

Intersection of A331892 and A331894.

Cf. A039724, A331891.

Sequence in context: A048700 A331892 A331893 * A164120 A342799 A043879

Adjacent sequences: A331892 A331893 A331894 * A331896 A331897 A331898

Keyword

nonn,base

Author

Amiram Eldar, Jan 30 2020

Status

approved