A317050 a(0) = 0 and for any n >= 0, a(n+1) is obtained by changing the rightmost possible digit in the negabinary representation of a(n) so as to get a value not yet in the sequence.

0, 1, -1, -2, 2, 3, 5, 4, -4, -3, -5, -6, -10, -9, -7, -8, 8, 9, 7, 6, 10, 11, 13, 12, 20, 21, 19, 18, 14, 15, 17, 16, -16, -15, -17, -18, -14, -13, -11, -12, -20, -19, -21, -22, -26, -25, -23, -24, -40, -39, -41, -42, -38, -37, -35, -36, -28, -27, -29, -30

Offset

0,4

Comments

Binary Gray code, interpreted as negabinary number.

This sequence is a bijection from nonnegative integers to signed integers.

This sequence has similarities with A317018; in both sequences, the negabinary representations of consecutive terms differ exactly by one digit.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..16383

Eric Weisstein's World of Mathematics, Negabinary.

Wikipedia, Negative base.

Formula

a(n) = A053985(A003188(n)).

Example

The first terms, alongside their negabinary representation, are:
  n   a(n)  nega(a(n))
  --  ----  ----------
   0     0        0
   1     1        1
   2    -1       11
   3    -2       10
   4     2      110
   5     3      111
   6     5      101
   7     4      100
   8    -4     1100
   9    -3     1101
  10    -5     1111
  11    -6     1110
  12   -10     1010
  13    -9     1011
  14    -7     1001
  15    -8     1000
  16     8    11000
  17     9    11001
  18     7    11011
  19     6    11010
  20    10    11110
a(8) = -4 because nega(a(7)) = 100. Changing the rightmost digit gives 101 of which the decimal value in the sequence. Similarily, changing to 110 and 000 gives no new term. Changing to 1100 does so a(8) is the decimal value of 1100 which is -4. - David A. Corneth, Jul 22 2018

Prog

(PARI) a(n) = fromdigits(binary(bitxor(n, n>>1)), -2)

Crossrefs

Cf. A003188, A039724, A053985, A212529, A317018.

Sequence in context: A359948 A289507 A076228 * A243970 A282443 A210554

Adjacent sequences: A317047 A317048 A317049 * A317051 A317052 A317053

Keyword

sign,look,base

Author

Rémy Sigrist, Jul 20 2018

Status

approved