A327191 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 abs(x - y).

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

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: abs(0 - 42) = 42,
   - "1" and "01010": x=1 and y=10: abs(1 - 10) = 9,
   - "10" and "1010": x=2 and y=10: abs(2 - 10) = 8,
   - "101" and "010": x=5 and y=2: abs(5 - 2) = 3,
   - "1010" and "10": x=10 and y=2: abs(10 - 2) = 8,
   - "10101" and "0": x=21 and y=0: abs(21 - 0) = 21,
   - "101010" and "": x=42 and y=0: abs(42 - 0) = 42,
- hence a(42) = 3.
		

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, abs(fromdigits(b[1..w],2) - fromdigits(b[w+1..#b],2)))); v

Formula

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