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For any n >= 0: consider all pairs of numbers (x, y) whose binary representations can be interleaved (or shuffled) to produce the binary representation of n (possibly with leading zeros); a(n) is the least possible value of x OR y (where OR denotes the bitwise OR operator).
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%I #7 Jan 05 2020 12:58:07

%S 0,1,1,1,1,1,3,3,1,1,2,3,2,3,3,3,1,1,2,3,2,3,3,3,3,3,3,3,6,7,7,7,1,1,

%T 2,3,2,3,3,3,3,3,3,3,5,5,7,7,3,3,3,3,5,5,6,7,6,7,6,7,6,7,7,7,1,1,2,3,

%U 2,3,3,3,3,3,3,3,5,5,7,7,3,3,3,3,5,5,6

%N For any n >= 0: consider all pairs of numbers (x, y) whose binary representations can be interleaved (or shuffled) to produce the binary representation of n (possibly with leading zeros); a(n) is the least possible value of x OR y (where OR denotes the bitwise OR operator).

%H Rémy Sigrist, <a href="/A330958/a330958.txt">C program for A330958</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%e For n = 5:

%e - the binary representation of 5 is "101",

%e - the possible values for (x, y), restricted to x >= y without loss of generality, are:

%e bin(5) x y x OR y

%e ------- - - ------

%e "101" 5 0 5

%e "1/01" 1 1 1

%e "10/1" 2 1 3

%e "1/0/1" 3 0 3

%e - hence a(5) = 1.

%o (C) See Links section.

%Y See A330925 for similar sequences.

%Y Cf. A327186.

%K nonn,base

%O 0,7

%A _Rémy Sigrist_, Jan 04 2020