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%I #13 Aug 26 2019 16:31:37
%S 0,1,1,1,1,1,3,3,1,1,2,3,3,3,3,3,1,1,2,3,5,5,6,7,3,3,3,3,7,7,7,7,1,1,
%T 2,3,4,5,6,7,5,5,7,7,5,5,7,7,3,3,3,3,6,7,6,7,7,7,7,7,7,7,7,7,1,1,2,3,
%U 4,5,6,7,9,9,10,11,12,13,14,15,5,5,7,7,5
%N 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 OR y (where OR denotes the bitwise OR operator).
%H Rémy Sigrist, <a href="/A327186/b327186.txt">Table of n, a(n) for n = 0..8192</a>
%F a(n) = 1 iff n = 2^k or n = 2^k + 1 for some k >= 0.
%e For n=42:
%e - the binary representation of 42 is "101010",
%e - there are 7 ways to split it:
%e - "" and "101010": x=0 and y=42: 0 OR 42 = 42,
%e - "1" and "01010": x=1 and y=10: 1 OR 10 = 11,
%e - "10" and "1010": x=2 and y=10: 2 OR 10 = 10,
%e - "101" and "010": x=5 and y=2: 5 OR 2 = 7,
%e - "1010" and "10": x=10 and y=2: 10 OR 2 = 10,
%e - "10101" and "0": x=21 and y=0: 21 OR 0 = 21,
%e - "101010" and "": x=42 and y=0: 42 OR 0 = 42,
%e - hence a(42) = 7.
%o (PARI) a(n) = my (v=oo, b=binary(n)); for (w=0, #b, v=min(v, bitor(fromdigits(b[1..w],2), fromdigits(b[w+1..#b],2)))); v
%Y Cf. A327187 (x XOR y variant), A327188 (x AND y variant).
%Y Cf. A327189 (x + y variant), A327190 (x * y variant), A327191 (x - y variant).
%Y Cf. A327192 (max(x, y) variant), A327193 (min(x, y) variant).
%Y Cf. A327194 (x^2 + y^2 variant), A327195 (x^2 - y^2 variant).
%K nonn,look,base
%O 0,7
%A _Rémy Sigrist_, Aug 25 2019
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