A331857 a(n) is the greatest value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

0, 1, 2, 3, 4, 6, 6, 7, 8, 12, 12, 14, 12, 14, 14, 15, 16, 24, 24, 28, 24, 26, 28, 30, 24, 28, 28, 30, 28, 30, 30, 31, 32, 48, 48, 56, 48, 52, 56, 60, 48, 52, 52, 58, 56, 58, 60, 62, 48, 56, 56, 60, 56, 58, 60, 62, 56, 60, 60, 62, 60, 62, 62, 63, 64, 96, 96

Offset

0,3

Links

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Rémy Sigrist, PARI program for A331857

Index entries for sequences related to binary expansion of n

Formula

a(n)^A023416(n) = A073138(n) (where a^k denotes the k-th iterate of n).

a(n) >= n with equality iff n belongs to A023758.

Example

For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
      "110" -> "011" -> 3
      "1" and "10" -> "1" and "01" -> 5
      "11" and "0" -> "11" and "0" -> 6
      "1" and "1" and "0" -> "1" and "1" and "0" -> 6
- we have 3 distinct values, the greatest being 6,
- hence a(6) = 6.

Prog

(PARI) See Links section.

Crossrefs

See A331855 for the number of distinct values, and A331856 for the least value.

Cf. A023416, A023758, A073138.

Sequence in context: A233569 A246593 A256999 * A073138 A342179 A362813

Adjacent sequences: A331854 A331855 A331856 * A331858 A331859 A331860

Keyword

nonn,base

Author

Rémy Sigrist, Jan 29 2020

Status

approved