OFFSET
0,4
COMMENTS
A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..8192
FORMULA
a(2^n - 1) = A000110(n).
EXAMPLE
The a(1) = 1 through a(9) = 7 maximal subsets:
{1} {12} {3} {34} {25} {16} {7} {78} {69}
{12} {124} {34} {25} {16} {168} {78}
{124} {34} {25} {258} {168}
{124} {34} {348} {249}
{124} {1248} {258}
{348}
{1248}
MATHEMATICA
binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
maxim[s_]:=Complement[s, Last/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]];
Table[Length[maxim[Select[Subsets[Range[n]], stableQ[#, Intersection[binpos[#1], binpos[#2]]!={}&]&]]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Mar 27 2019
EXTENSIONS
a(15)-a(61) from Alois P. Heinz, Mar 28 2019
STATUS
approved