A327187 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 XOR y (where XOR denotes the bitwise XOR operator).

0, 1, 1, 0, 1, 0, 3, 2, 1, 0, 0, 1, 3, 2, 1, 0, 1, 0, 0, 1, 5, 4, 4, 5, 3, 2, 1, 0, 7, 6, 5, 4, 1, 0, 0, 1, 0, 1, 2, 3, 5, 4, 7, 6, 1, 0, 3, 2, 3, 2, 1, 0, 2, 3, 0, 1, 7, 6, 5, 4, 3, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 3, 9, 8, 8, 9, 8, 9, 10, 11, 5, 4, 7, 6, 1, 0

Offset

0,7

Links

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

Formula

a(n) = 0 iff n = 0 or n belongs to A175468.

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 XOR 42 = 42,
   - "1" and "01010": x=1 and y=10: 1 XOR 10 = 11,
   - "10" and "1010": x=2 and y=10: 2 XOR 10 = 8,
   - "101" and "010": x=5 and y=2: 5 XOR 2 = 7,
   - "1010" and "10": x=10 and y=2: 10 XOR 2 = 8,
   - "10101" and "0": x=21 and y=0: 21 XOR 0 = 21,
   - "101010" and "": x=42 and y=0: 42 XOR 0 = 42,
- hence a(42) = 7.

Prog

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

Crossrefs

See A327186 for other variants.

Cf. A175468.

Sequence in context: A058257 A330959 A083199 * A274537 A305234 A021761

Adjacent sequences: A327184 A327185 A327186 * A327188 A327189 A327190

Keyword

nonn,look,base

Author

Rémy Sigrist, Aug 25 2019

Status

approved