A327195 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^2 - y^2).

0, 1, 1, 0, 1, 0, 3, 8, 1, 0, 0, 5, 9, 8, 5, 0, 1, 0, 0, 5, 12, 21, 21, 16, 9, 8, 5, 0, 7, 16, 27, 40, 1, 0, 0, 5, 0, 9, 20, 33, 25, 24, 21, 16, 9, 0, 11, 24, 9, 8, 5, 0, 7, 11, 0, 13, 49, 48, 45, 40, 33, 24, 13, 0, 1, 0, 0, 5, 0, 9, 20, 15, 48, 65, 77, 72, 65

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(0^2 - 42^2) = 1764,
   - "1" and "01010": x=1 and y=10: abs(1^2 - 10^2) = 99,
   - "10" and "1010": x=2 and y=10: abs(2^2 - 10^2) = 96,
   - "101" and "010": x=5 and y=2: abs(5^2 - 2^2) = 21,
   - "1010" and "10": x=10 and y=2: abs(10^2 - 2^2) = 96,
   - "10101" and "0": x=21 and y=0: abs(21^2 - 0^2) = 441,
   - "101010" and "": x=42 and y=0: abs(42^2 - 0^2) = 1764,
- hence a(42) = 21.
		

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

Formula

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

a(n) = 1 iff n is a power of 2.