A331893 Positive numbers k such that both k and -k are a palindromes in negabinary representation.

1, 5, 7, 17, 21, 31, 57, 65, 85, 127, 155, 217, 257, 273, 325, 341, 455, 511, 635, 857, 889, 993, 1025, 1105, 1253, 1285, 1365, 1799, 2047, 2159, 2555, 2667, 3417, 3577, 3641, 3937, 4097, 4161, 4369, 4433, 4965, 5125, 5189, 5397, 5461, 6951, 7175, 7967, 8191

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..10000

Example

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

Mathematica

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]

Crossrefs

Intersection of A331891 and A331892.

Cf. A005352, A039724, A212529.

Sequence in context: A146949 A048700 A331892 * A331895 A164120 A342799

Adjacent sequences: A331890 A331891 A331892 * A331894 A331895 A331896

Keyword

nonn,base

Author

Amiram Eldar, Jan 30 2020

Status

approved