A396694 Lexicographically earliest sequence of distinct nonnegative integers such that each pixel in the binary plot of the sequence is within a knights' move's distance from another pixel.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 25, 26, 24, 27, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 49, 50, 48, 51, 36, 37, 38, 39, 52, 53, 54, 55, 40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67

Offset

0,3

Comments

A variant of A394166 where each pixel, say a pixel related to a(n), is attacked by some pixel related to a(k) with k in max(0, n-2)..n+2. In other words, if 2^k appears in the binary expansion of a(n), then for some k', n' such that {abs(n-n'), abs(k-k')} = {1, 2}, 2^k' appears in the binary expansion of a(n').

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, Binary plot of the sequence for n = 0..512

Rémy Sigrist, C++ program

Formula

Empirically, for any k >= 0, a(n) < 2^k iff n < 2^k.

Example

The first terms, alongside their binary expansions with dots instead of zeros, are:
  n   a(n)  bin(a(n))
  --  ----  ------------------
   0     0                   .
   1     1                   1
   2     2                  1.
   3     3                  11
   4     4                 1..
   5     5                 1.1
   6     6                 11.
   7     7                 111
   8     8                1...
   9     9                1..1
  10    10                1.1.
  11    11                1.11
  12    12                11..
  13    13                11.1
  14    14                111.
  15    15                1111
  16    16               1....
  17    17               1...1
  18    18               1..1.
  19    19               1..11
  20    25               11..1
  21    26               11.1.
  22    24               11...
  23    27               11.11

Prog

(C++) // See Links section.

Crossrefs

Cf. A394166.

Sequence in context: A247759 A377912 A326872 * A110548 A249815 A250244

Adjacent sequences: A396688 A396689 A396691 * A396695 A396704 A396705

Keyword

nonn,base

Author

Rémy Sigrist, Jun 02 2026

Status

approved