A207676 - OEIS

%I #23 Jan 04 2021 19:52:33

%S 0,1,1,2,1,2,2,1,1,2,2,1,2,1,1,0,1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,1,2,

%T 2,1,2,1,1,2,2,1,1,2,1,2,2,1,2,1,1,0,1,2,2,1,1,2,2,1,0,1,1,2,1,2,2,1,

%U 2,1,1,2,2,1,1,2,1,2,2,1,2,1,1,2,1,0,2

%N Nonlinearities of 3-variable Boolean functions ordered lexicographically.

%C Nonlinearity of a Boolean function is its minimum Hamming distance to the elements of the set of affine Boolean functions.

%C In this sequence, n represents the truth table of Boolean functions.

%C There are 2^2^3 = 256 terms in this list, i.e., the number of Boolean functions of 3-variables.

%C Also the list of first 2^2^3 terms of r-th order nonlinearity values of Boolean functions of (r+2)-variables in lexicographic order of their truth tables.

%H Erdener Uyan, <a href="/A207676/b207676.txt">Table of n, a(n) for n = 0..255</a> (complete sequence)

%e n in GF(2^3) a(1)=a((00000001)_2)=1;a(5)=a((00000101)_2)=2;a(15)=a((00001111)_2)=0;

%e This can be written as a triangle, though having few outliers:

%e 0,

%e 1,

%e 1,2,

%e 1,2,2,1,

%e 1,2,2,1,2,1,1,0,

%e 1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,

%e 1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,2,1,1,0,1,2,2,1,1,2,2,1,0,1,1,2,...

%o (R w/ boolfun package)

%o for(n in 0:2^(2^3)-1){

%o f<- BooleanFunction(toBin(n,2^3))

%o a[n]<-nl(f)

%o }

%Y Cf. A000120, A000069, A001969, A007088 (sequences dealing with binary expansion of n).

%Y Cf. A051253, A053168, A053189 (sequences that relate nonlinearity with Hamming weight for a special class of Boolean functions).

%K nonn,fini,full

%O 0,4

%A _Erdener Uyan_, Feb 19 2012