A327193 For any n >= 0: consider the different ways to split the binary representation of n into two (possibly empty) parts, say with value x and y; a(n) is the greatest possible value of min(x, y).

0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 3, 0, 1, 2, 3, 2, 2, 2, 3, 1, 1, 2, 3, 3, 3, 3, 3, 0, 1, 2, 3, 4, 4, 4, 4, 2, 2, 2, 3, 4, 5, 5, 5, 1, 1, 2, 3, 4, 5, 6, 6, 3, 3, 3, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 4, 4, 4, 4, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 6

Offset

0,11

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Formula

a(n) = 0 iff n = 0 or n is a power of 2.

Example

For n=42:
- the binary representation of 42 is "101010",
- there are 7 ways to split it:
   - "" and "101010": x=0 and y=42: min(0, 42) = 0,
   - "1" and "01010": x=1 and y=10: min(1, 10) = 1,
   - "10" and "1010": x=2 and y=10: min(2, 10) = 2,
   - "101" and "010": x=5 and y=2: min(5, 2) = 2,
   - "1010" and "10": x=10 and y=2: min(10, 2) = 2,
   - "10101" and "0": x=21 and y=0: min(21, 0) = 0,
   - "101010" and "": x=42 and y=0: min(42, 0) = 0,
- hence a(42) = 2.

Prog

(PARI) a(n) = my (v=-oo, b=binary(n)); for (w=0, #b, v=max(v, min(fromdigits(b[1..w], 2), fromdigits(b[w+1..#b], 2)))); v

Crossrefs

See A327186 for other variants.

Sequence in context: A351706 A016533 A122915 * A279522 A182592 A030298

Adjacent sequences: A327190 A327191 A327192 * A327194 A327195 A327196

Keyword

nonn,look,base

Author

Rémy Sigrist, Aug 25 2019

Status

approved