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 A207676 Nonlinearities of 3-variable Boolean functions ordered lexicographically. 2
 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, 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, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Nonlinearity of a Boolean function is its minimum Hamming distance to the elements of the set of affine Boolean functions. In this sequence, n represents the truth table of Boolean functions. There are 2^2^3 = 256 terms in this list, i.e., the number of Boolean functions of 3-variables. 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. LINKS Erdener Uyan, Table of n, a(n) for n = 0..255 (complete sequence) EXAMPLE n in GF(2^3) a(1)=a((00000001)_2)=1;a(5)=a((00000101)_2)=2;a(15)=a((00001111)_2)=0; This can be written as a triangle, though having few outliers: 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, 1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,2,1,1,0,1,2,2,1,1,2,2,1,0,1,1,2,... PROG (R w/ boolfun package) for(n in 0:2^(2^3)-1){ f<- BooleanFunction(toBin(n, 2^3)) a[n]<-nl(f) } CROSSREFS Cf. A000120, A000069, A001969, A007088 (sequences dealing with binary expansion of n). Cf. A051253, A053168, A053189 (sequences that relate nonlinearity with Hamming weight for a special class of Boolean functions). Sequence in context: A054350 A026606 A265918 * A161175 A356515 A095955 Adjacent sequences: A207673 A207674 A207675 * A207677 A207678 A207679 KEYWORD nonn,fini,full AUTHOR Erdener Uyan, Feb 19 2012 STATUS approved

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Last modified December 10 22:05 EST 2023. Contains 367717 sequences. (Running on oeis4.)