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

Author

Rémy Sigrist, Aug 25 2019

Keywords

• nonn
• look
• base

Examples

			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.
		

Links

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

Crossrefs

See A327186 for other variants.

Cf. A175468.

Programs

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

Formula

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