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

0,3

Comments

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

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

Formula

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

Example

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)

Prog

(PARI) See Links section.

Crossrefs

Cf. A005811, A180200, A227736.

Sequence in context: A330647 A209260 A297409 * A137760 A368428 A360600

Adjacent sequences: A335855 A335856 A335857 * A335859 A335860 A335861

Keyword

nonn,base

Author

Rémy Sigrist, Jun 27 2020

Status

approved