cp's OEIS Frontend

A371294 Numbers whose binary indices are connected and pairwise indivisible, where two numbers are connected iff they have a common factor. A hybrid ranking sequence for connected antichains of multisets.

%I A371294 #5 Mar 30 2024 15:59:49
%S A371294 1,2,4,8,16,32,40,64,128,160,256,288,296,416,512,520,544,552,640,672,
%T A371294 800,808,928,1024,2048,2176,2304,2432,2560,2688,2816,2944,4096,8192,
%U A371294 8200,8224,8232,8320,8352,8480,8488,8608,8704,8712,8736,8744,8832,8864,8992
%N A371294 Numbers whose binary indices are connected and pairwise indivisible, where two numbers are connected iff they have a common factor. A hybrid ranking sequence for connected antichains of multisets.
%C A371294 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A371294 A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
%F A371294 Intersection of A087086 and A371291.
%e A371294 The terms together with their prime indices of binary indices begin:
%e A371294     1: {{}}
%e A371294     2: {{1}}
%e A371294     4: {{2}}
%e A371294     8: {{1,1}}
%e A371294    16: {{3}}
%e A371294    32: {{1,2}}
%e A371294    40: {{1,1},{1,2}}
%e A371294    64: {{4}}
%e A371294   128: {{1,1,1}}
%e A371294   160: {{1,2},{1,1,1}}
%e A371294   256: {{2,2}}
%e A371294   288: {{1,2},{2,2}}
%e A371294   296: {{1,1},{1,2},{2,2}}
%e A371294   416: {{1,2},{1,1,1},{2,2}}
%e A371294   512: {{1,3}}
%e A371294   520: {{1,1},{1,3}}
%e A371294   544: {{1,2},{1,3}}
%e A371294   552: {{1,1},{1,2},{1,3}}
%e A371294   640: {{1,1,1},{1,3}}
%e A371294   672: {{1,2},{1,1,1},{1,3}}
%e A371294   800: {{1,2},{2,2},{1,3}}
%e A371294   808: {{1,1},{1,2},{2,2},{1,3}}
%e A371294   928: {{1,2},{1,1,1},{2,2},{1,3}}
%t A371294 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A371294 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A371294 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A371294 Select[Range[1000],stableQ[bpe[#],Divisible]&&connectedQ[prix/@bpe[#]]&]
%Y A371294 Connected case of A087086, relatively prime A328671.
%Y A371294 For binary indices of binary indices we have A326750, non-primitive A326749.
%Y A371294 For prime indices of prime indices we have A329559, non-primitive A305078.
%Y A371294 Primitive case of A371291 = positions of ones in A371452.
%Y A371294 For binary indices of prime indices we have A371445, non-primitive A325118.
%Y A371294 A001187 counts connected graphs.
%Y A371294 A007718 counts non-isomorphic connected multiset partitions.
%Y A371294 A048143 counts connected antichains of sets.
%Y A371294 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A371294 A070939 gives length of binary expansion.
%Y A371294 A096111 gives product of binary indices.
%Y A371294 A326964 counts connected set-systems, covering A323818.
%Y A371294 Cf. A001222, A051026, A285572, A303362, A304713, A305079, A316476, A319496, A319719, A326704, A371446.
%K A371294 nonn
%O A371294 1,2
%A A371294 _Gus Wiseman_, Mar 28 2024