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

Author

Rémy Sigrist, Jan 29 2020

Keywords

• nonn
• base

Examples

			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.
		

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

Crossrefs

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

Cf. A000225, A023416, A038573.

Programs

PARI

See Links section.

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.