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A326781
No position of a 1 in the reversed binary expansion of n is a power of 2.
6
0, 4, 16, 20, 32, 36, 48, 52, 64, 68, 80, 84, 96, 100, 112, 116, 256, 260, 272, 276, 288, 292, 304, 308, 320, 324, 336, 340, 352, 356, 368, 372, 512, 516, 528, 532, 544, 548, 560, 564, 576, 580, 592, 596, 608, 612, 624, 628, 768, 772, 784, 788, 800, 804, 816
OFFSET
1,2
COMMENTS
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:
0: {}
4: {{1,2}}
16: {{1,3}}
20: {{1,2},{1,3}}
32: {{2,3}}
36: {{1,2},{2,3}}
48: {{1,3},{2,3}}
52: {{1,2},{1,3},{2,3}}
64: {{1,2,3}}
68: {{1,2},{1,2,3}}
80: {{1,3},{1,2,3}}
84: {{1,2},{1,3},{1,2,3}}
96: {{2,3},{1,2,3}}
100: {{1,2},{2,3},{1,2,3}}
112: {{1,3},{2,3},{1,2,3}}
116: {{1,2},{1,3},{2,3},{1,2,3}}
256: {{1,4}}
260: {{1,2},{1,4}}
272: {{1,3},{1,4}}
276: {{1,2},{1,3},{1,4}}
FORMULA
Conjectures from Colin Barker, Jul 27 2019: (Start)
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)).
a(n) = a(n-1) + a(n-16) - a(n-17) for n>17.
(End)
EXAMPLE
The binary indices of n are row n of A048793. The sequence of terms together with their binary indices begins:
0: {}
4: {3}
16: {5}
20: {3,5}
32: {6}
36: {3,6}
48: {5,6}
52: {3,5,6}
64: {7}
68: {3,7}
80: {5,7}
84: {3,5,7}
96: {6,7}
100: {3,6,7}
112: {5,6,7}
116: {3,5,6,7}
256: {9}
260: {3,9}
272: {5,9}
276: {3,5,9}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], !MemberQ[Length/@bpe/@bpe[#], 1]&]
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved