A327186 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 least possible value of x OR y (where OR denotes the bitwise OR operator).

0, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 3, 3, 3, 3, 3, 1, 1, 2, 3, 5, 5, 6, 7, 3, 3, 3, 3, 7, 7, 7, 7, 1, 1, 2, 3, 4, 5, 6, 7, 5, 5, 7, 7, 5, 5, 7, 7, 3, 3, 3, 3, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 1, 2, 3, 4, 5, 6, 7, 9, 9, 10, 11, 12, 13, 14, 15, 5, 5, 7, 7, 5

Offset

0,7

Links

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

Formula

a(n) = 1 iff n = 2^k or n = 2^k + 1 for some k >= 0.

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: 0 OR 42 = 42,
   - "1" and "01010": x=1 and y=10: 1 OR 10 = 11,
   - "10" and "1010": x=2 and y=10: 2 OR 10 = 10,
   - "101" and "010": x=5 and y=2: 5 OR 2 = 7,
   - "1010" and "10": x=10 and y=2: 10 OR 2 = 10,
   - "10101" and "0": x=21 and y=0: 21 OR 0 = 21,
   - "101010" and "": x=42 and y=0: 42 OR 0 = 42,
- hence a(42) = 7.

Prog

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

Crossrefs

Cf. A327187 (x XOR y variant), A327188 (x AND y variant).

Cf. A327189 (x + y variant), A327190 (x * y variant), A327191 (x - y variant).

Cf. A327192 (max(x, y) variant), A327193 (min(x, y) variant).

Cf. A327194 (x^2 + y^2 variant), A327195 (x^2 - y^2 variant).

Sequence in context: A098505 A178395 A330958 * A021306 A214281 A125300

Adjacent sequences: A327183 A327184 A327185 * A327187 A327188 A327189

Keyword

nonn,look,base

Author

Rémy Sigrist, Aug 25 2019

Status

approved