cp's OEIS Frontend

A326781 No position of a 1 in the reversed binary expansion of n is a power of 2.

%I A326781 #12 Jul 27 2019 14:51:27
%S A326781 0,4,16,20,32,36,48,52,64,68,80,84,96,100,112,116,256,260,272,276,288,
%T A326781 292,304,308,320,324,336,340,352,356,368,372,512,516,528,532,544,548,
%U A326781 560,564,576,580,592,596,608,612,624,628,768,772,784,788,800,804,816
%N A326781 No position of a 1 in the reversed binary expansion of n is a power of 2.
%C A326781 Also BII-numbers (see A326031) of set-systems with no singleton edges. For example, the sequence of such set-systems together with their BII-numbers begins:
%C A326781     0: {}
%C A326781     4: {{1,2}}
%C A326781    16: {{1,3}}
%C A326781    20: {{1,2},{1,3}}
%C A326781    32: {{2,3}}
%C A326781    36: {{1,2},{2,3}}
%C A326781    48: {{1,3},{2,3}}
%C A326781    52: {{1,2},{1,3},{2,3}}
%C A326781    64: {{1,2,3}}
%C A326781    68: {{1,2},{1,2,3}}
%C A326781    80: {{1,3},{1,2,3}}
%C A326781    84: {{1,2},{1,3},{1,2,3}}
%C A326781    96: {{2,3},{1,2,3}}
%C A326781   100: {{1,2},{2,3},{1,2,3}}
%C A326781   112: {{1,3},{2,3},{1,2,3}}
%C A326781   116: {{1,2},{1,3},{2,3},{1,2,3}}
%C A326781   256: {{1,4}}
%C A326781   260: {{1,2},{1,4}}
%C A326781   272: {{1,3},{1,4}}
%C A326781   276: {{1,2},{1,3},{1,4}}
%F A326781 Conjectures from _Colin Barker_, Jul 27 2019: (Start)
%F A326781 G.f.: 4*x^2*(1 + 3*x + x^2 + 3*x^3 + x^4 + 3*x^5 + x^6 + 3*x^7 + x^8 + 3*x^9 + x^10 + 3*x^11 + x^12 + 3*x^13 + x^14 + 35*x^15) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)).
%F A326781 a(n) = a(n-1) + a(n-16) - a(n-17) for n>17.
%F A326781 (End)
%e A326781 The binary indices of n are row n of A048793. The sequence of terms together with their binary indices begins:
%e A326781     0: {}
%e A326781     4: {3}
%e A326781    16: {5}
%e A326781    20: {3,5}
%e A326781    32: {6}
%e A326781    36: {3,6}
%e A326781    48: {5,6}
%e A326781    52: {3,5,6}
%e A326781    64: {7}
%e A326781    68: {3,7}
%e A326781    80: {5,7}
%e A326781    84: {3,5,7}
%e A326781    96: {6,7}
%e A326781   100: {3,6,7}
%e A326781   112: {5,6,7}
%e A326781   116: {3,5,6,7}
%e A326781   256: {9}
%e A326781   260: {3,9}
%e A326781   272: {5,9}
%e A326781   276: {3,5,9}
%t A326781 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A326781 Select[Range[100],!MemberQ[Length/@bpe/@bpe[#],1]&]
%Y A326781 Cf. A000120, A029931, A048793, A062289, A070939, A326031, A326782, A326788.
%K A326781 nonn,base
%O A326781 1,2
%A A326781 _Gus Wiseman_, Jul 25 2019