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 A325096 Number of maximal subsets of {1...n} with no binary carries. 17
 1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 12, 13, 14, 15, 15, 20, 25, 27, 32, 34, 36, 37, 42, 44, 46, 47, 49, 50, 51, 52, 52, 67, 82, 87, 102, 107, 112, 114, 129, 134, 139, 141, 146, 148, 150, 151, 166, 171, 176, 178, 183, 185, 187, 188, 193, 195, 197, 198, 200, 201 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000110, A019565, A050315, A080572, A247935, A267610, A267700. Cf. A325095, A325099, A325100, A325101, A325103, A325104, A325107. Sequence in context: A340276 A340275 A342499 * A261771 A015743 A015755 Adjacent sequences:  A325093 A325094 A325095 * A325097 A325098 A325099 KEYWORD nonn,look AUTHOR Gus Wiseman, Mar 27 2019 EXTENSIONS a(15)-a(61) from Alois P. Heinz, Mar 28 2019 STATUS approved

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Last modified June 21 06:24 EDT 2021. Contains 345358 sequences. (Running on oeis4.)