A335858 Nonnegative integers ordered by binary length and then lexicographically by run lengths (considering least significant runs first).

0, 1, 2, 3, 5, 6, 4, 7, 10, 13, 9, 14, 11, 12, 8, 15, 21, 26, 18, 29, 22, 25, 17, 30, 20, 27, 19, 28, 23, 24, 16, 31, 42, 53, 37, 58, 45, 50, 34, 61, 41, 54, 38, 57, 46, 49, 33, 62, 43, 52, 36, 59, 44, 51, 35, 60, 40, 55, 39, 56, 47, 48, 32, 63, 85, 106, 74

Offset: 0

Author

Rémy Sigrist, Jun 27 2020

Keywords

• nonn
• base

Comments

The variant where we consider most significant runs first apparently corresponds to A180200.

Examples

			The first terms, alongside the corresponding binary representation and run lengths, are:
  n   a(n)  bin(a(n))  A227736(n, *)
  --  ----  ---------  -------------
   0     0          0  ()
   1     1          1  (1)
   2     2         10  (1, 1)
   3     3         11  (2)
   4     5        101  (1, 1, 1)
   5     6        110  (1, 2)
   6     4        100  (2, 1)
   7     7        111  (3)
   8    10       1010  (1, 1, 1, 1)
   9    13       1101  (1, 1, 2)
  10     9       1001  (1, 2, 1)
  11    14       1110  (1, 3)
  12    11       1011  (2, 1, 1)
  13    12       1100  (2, 2)
  14     8       1000  (3, 1)
  15    15       1111  (4)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, PARI program for A335858
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A005811, A180200, A227736.

Programs

PARI

See Links section.

Formula

Apparently a(n) = A056539(A180200(n)).