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

Author

Rémy Sigrist, Aug 09 2025

Keywords

• nonn
• tabf
• base

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.

Examples

			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
		

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

Crossrefs

See A385661 for a similar sequence.

Cf. A358875, A387024 (inverse).

Programs

PARI

\\ See Links section.