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

1,4

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.

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A039724, A163252, A212529, A316995.

Sequence in context: A053811 A350167 A049840 * A072039 A204012 A131901

Adjacent sequences: A317015 A317016 A317017 * A317019 A317020 A317021

Keyword

sign,base

Author

Rémy Sigrist, Jul 19 2018

Status

approved