A316995 Sequence of distinct signed integers such that a(1) = 0 and for any n > 0, a(n+1) is of the form a(n) + (-2)^k (where k >= 0) and has the smallest possible absolute value (in case of a tie, minimize k).

0, 1, -1, -3, -2, 2, 3, 4, -4, -6, -5, -7, -9, 7, 5, 6, 10, 8, 9, 13, 11, 12, 16, 14, 15, -17, -13, -12, -8, -10, -18, -14, -16, -15, -11, -19, -21, -20, -22, -24, -23, -25, -27, -26, -28, -30, -29, -31, -33, 31, 23, 21, 19, 17, 18, 22, 20, 24, 25, 26, 27, 28

Offset

1,4

Comments

This sequence is likely to contain every signed integer.

Links

Table of n, a(n) for n=1..62.

Rémy Sigrist, PARI program for A316995

Example

The first terms, alongside the value k such that a(n+1) = a(n) + (-2)^k, are:
  n  a(n)   k
  -- ----   --
   1    0    0
   2    1    1
   3   -1    1
   4   -3    0
   5   -2    2
   6    2    0
   7    3    0
   8    4    3
   9   -4    1
  10   -6    0
  11   -5    1
  12   -7    1
  13   -9    4
  14    7    1
  15    5    0
  16    6    2
  17   10    1
  18    8    0
  19    9    2
  20   13    1

Prog

(PARI) See Links section.

Crossrefs

Cf. A122803.

Sequence in context: A046822 A129001 A029246 * A338241 A222456 A222673

Adjacent sequences: A316992 A316993 A316994 * A316996 A316997 A316998

Keyword

sign

Author

Rémy Sigrist, Jul 18 2018

Status

approved