A331856 a(n) is the least value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 5, 7, 3, 7, 7, 15, 1, 3, 5, 7, 5, 11, 11, 15, 3, 7, 11, 15, 7, 15, 15, 31, 1, 3, 5, 7, 9, 11, 11, 15, 5, 11, 21, 23, 13, 23, 23, 31, 3, 7, 13, 15, 11, 23, 27, 31, 7, 15, 23, 31, 15, 31, 31, 63, 1, 3, 5, 7, 9, 11, 11, 15, 9, 19, 21

Offset

0,4

Links

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

Rémy Sigrist, PARI program for A331856

Index entries for sequences related to binary expansion of n

Formula

a(n)^A023416(n) = A038573(n) (where a^k denotes the k-th iterate of a).

a(n) <= n with equality iff n belongs to A000225.

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 least being 3,
- hence a(6) = 3.

Prog

(PARI) See Links section.

Crossrefs

See A331855 for the number of distinct values, and A331857 for the greatest value.

Cf. A000225, A023416, A038573.

Sequence in context: A151837 A356354 A355339 * A163381 A327190 A160123

Adjacent sequences: A331853 A331854 A331855 * A331857 A331858 A331859

Keyword

nonn,base

Author

Rémy Sigrist, Jan 29 2020

Status

approved