This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056287 #29 Jul 22 2025 05:52:23 %S A056287 1,3,9,15,28 %N A056287 Maximal AND-OR formula complexity (operator count) for n-input Boolean functions. %C A056287 a(n) = minimal number of edges in 2-terminal series-parallel switching network (where edges are labeled with the variables X_i and X_i') which achieves the worst f. %C A056287 Consider all 2^2^n Boolean functions f of n variables X_1, ..., X_n; the X_i's and their negated values X_1', ..., X_n' are available and we must realize f using AND's and OR's of these 2n variables with the smallest total number of AND's and OR's; call the minimal total number of AND's and OR's used G(f); then a(n) = max G(f). %H A056287 Russ Cox, <a href="/A056287/a056287.txt">Notes on computing a(4)</a> %H A056287 Russ Cox, <a href="http://research.swtch.com/boolean">Minimum Boolean Formulas</a> %e A056287 For n=2 a worst f is X XOR Y, which can be realized by X AND Y' OR X' AND Y = XY' + X'Y. %e A056287 For n=3 a worst f is X XOR Y XOR Z, which can be realized by (X*Z'+X'*Z+Y')*(X*Z+X'*Z'+Y). %e A056287 For n=4 a worst f is W XOR X XOR Y XOR Z, which can be realized by ((X XOR Z)'+(W XOR Y)')*((X XOR Z)+(W XOR Y)) = (X*Z'+X'*Z+W'*Y+W*Y')*(X*Z+X'*Z'+W*Y+W'*Y'). %e A056287 For n=5 there are three worst f's up to permutation and negation of input variables. They have 32-bit truth tables 0x16686997, 0x16696997 and 0x1669e996 (in hexadecimal). %Y A056287 Cf. A058759, A057241, A178939. %K A056287 nonn,nice,hard,more %O A056287 1,2 %A A056287 _N. J. A. Sloane_, Jan 05 2001 %E A056287 a(3) and a(4) computed by _Russ Cox_, Jan 03 2001 %E A056287 a(5) computed by _Russ Cox_ and _Alexander D. Healy_, Jul 12 2010