A331892 -id:A331892 - cp's OEIS frontend

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

Amiram Eldar, Jan 30 2020

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A331891 and A331892.

Cf. A005352, A039724, A212529.

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]

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

Original entry on oeis.org

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

Amiram Eldar, Jan 30 2020

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

			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.

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

Intersection of A006995 and A331893.
Intersection of A331892 and A331894.
Cf. A039724, A331891.

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[#] &]

cp's OEIS Frontend

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

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