A317018 Sequence of distinct signed integers such that a(1) = 0 and for any n > 0, the negabinary representation of a(n+1) differ by exactly one digit from the negabinary representation of a(n) and has the smallest possible absolute value (in case of a tie, choose the integer with the rightmost difference).

0, 1, -1, -2, 2, 3, 5, -3, -4, 4, 20, 12, 8, 6, 7, 9, -7, -8, -10, -6, -5, -9, -41, 23, 22, 24, 25, 29, 27, 26, 28, 36, -28, -12, -11, -13, -14, -18, 14, 15, 17, -15, -16, 16, 80, 48, 32, 30, 31, 33, -31, -27, -29, -30, -34, -32, -40, -24, -20, -19, 13, 11, 10

Offset: 1

Author

Rémy Sigrist, Jul 19 2018

Keywords

• sign
• base

Comments

This sequence has similarities with A316995; in both sequences, the absolute value of the difference of two consecutive terms is a power of 2.

This sequence also has similarities with A163252.

Examples

			The first terms, alongside their negabinary representation, are:
  n   a(n)  nega(a(n))
  --  ----  ----------
   1     0        0
   2     1        1
   3    -1       11
   4    -2       10
   5     2      110
   6     3      111
   7     5      101
   8    -3     1101
   9    -4     1100
  10     4      100
  11    20    10100
  12    12    11100
  13     8    11000
  14     6    11010
  15     7    11011
  16     9    11001
  17    -7     1001
  18    -8     1000
  19   -10     1010
  20    -6     1110
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Line plot of the first 10000 terms
• Rémy Sigrist, PARI program for A317018
• Eric Weisstein's World of Mathematics, Negabinary.
• Wikipedia, Negative base.

Crossrefs

Cf. A039724, A163252, A212529, A316995.

Programs

PARI

See Links section.