A386932 Lexicographically earliest sequence of distinct positive integers that can be partitioned into runs of integers without common bits, the n-th such run having a(n) terms.

1, 2, 4, 3, 8, 16, 32, 5, 10, 48, 6, 9, 64, 128, 256, 512, 1024, 2048, 7, 24, 96, 384, 1536, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 11, 20, 160, 320, 2560, 5120, 24576, 98304, 393216, 1572864, 6291456, 8388608

Offset

1,2

Comments

This sequence is a permutation of the positive integers as each run starts with the least integer not yet in the sequence.

The powers of two appear in natural order.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..6223

Rémy Sigrist, Logarithmic scatterplot of the first 10319 terms (where red pixels correspond to powers of 2)

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms and runs are:
  n  a(n)  n-th run
  -  ----  -----------------------------------
  1     1  1
  2     2  2, 4
  3     4  3, 8, 16, 32
  4     3  5, 10, 48
  5     8  6, 9, 64, 128, 256, 512, 1024, 2048

Prog

(PARI) \\ See Links section.

Crossrefs

See A385661 for a similar sequence.

Cf. A358875, A387024 (inverse).

Sequence in context: A246679 A244153 A366347 * A308328 A277415 A243051

Adjacent sequences: A386929 A386930 A386931 * A386933 A386934 A386935

Keyword

nonn,tabf,base

Author

Rémy Sigrist, Aug 09 2025

Status

approved