cp's OEIS Frontend

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).

%I A327187 #12 Aug 26 2019 16:30:42
%S A327187 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,
%T A327187 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,
%U A327187 0,1,2,3,9,8,8,9,8,9,10,11,5,4,7,6,1,0
%N 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).
%H A327187 Rémy Sigrist, <a href="/A327187/b327187.txt">Table of n, a(n) for n = 0..8192</a>
%F A327187 a(n) = 0 iff n = 0 or n belongs to A175468.
%e A327187 For n=42:
%e A327187 - the binary representation of 42 is "101010",
%e A327187 - there are 7 ways to split it:
%e A327187    - "" and "101010": x=0 and y=42: 0 XOR 42 = 42,
%e A327187    - "1" and "01010": x=1 and y=10: 1 XOR 10 = 11,
%e A327187    - "10" and "1010": x=2 and y=10: 2 XOR 10 = 8,
%e A327187    - "101" and "010": x=5 and y=2: 5 XOR 2 = 7,
%e A327187    - "1010" and "10": x=10 and y=2: 10 XOR 2 = 8,
%e A327187    - "10101" and "0": x=21 and y=0: 21 XOR 0 = 21,
%e A327187    - "101010" and "": x=42 and y=0: 42 XOR 0 = 42,
%e A327187 - hence a(42) = 7.
%o A327187 (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
%Y A327187 See A327186 for other variants.
%Y A327187 Cf. A175468.
%K A327187 nonn,look,base
%O A327187 0,7
%A A327187 _Rémy Sigrist_, Aug 25 2019