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A295277
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a(n) = number of distinct earlier terms that have no common one bit with n in binary representation.
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3
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0, 1, 1, 2, 2, 2, 1, 3, 2, 2, 1, 4, 2, 2, 1, 5, 3, 4, 2, 4, 2, 2, 1, 6, 4, 4, 2, 4, 2, 2, 1, 7, 4, 4, 2, 4, 2, 2, 1, 8, 4, 4, 2, 4, 2, 2, 1, 9, 5, 6, 3, 6, 3, 4, 2, 8, 4, 4, 2, 4, 2, 2, 1, 10, 6, 6, 3, 7, 4, 4, 2, 8, 4, 4, 2, 4, 2, 2, 1, 11, 6, 6, 3, 8, 4, 4
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OFFSET
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1,4
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COMMENTS
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This sequence is a variant of A295276: here we count earlier terms without multiplicity, there with multiplicity.
The scatterplot of the first terms has fractal features (see scatterplot in Links section); see also A295283 for a variant of this sequence.
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LINKS
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FORMULA
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a(n) = #{ a(k) such that 0 < k < n and a(k) AND n = 0 } (where AND stands for the bitwise AND operator).
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EXAMPLE
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The first terms, alongside the distinct earlier terms with no common one bit with n, are:
n a(n) Distinct earlier terms with no common one bit with n
-- ---- ----------------------------------------------------
1 0 {}
2 1 {0}
3 1 {0}
4 2 {0, 1}
5 2 {0, 2}
6 2 {0, 1}
7 1 {0}
8 3 {0, 1, 2}
9 2 {0, 2}
10 2 {0, 1}
11 1 {0}
12 4 {0, 1, 2, 3}
13 2 {0, 2}
14 2 {0, 1}
15 1 {0}
16 5 {0, 1, 2, 3, 4}
17 3 {0, 2, 4}
18 4 {0, 1, 4, 5}
19 2 {0, 4}
20 4 {0, 1, 2, 3}
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PROG
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(PARI) mx=-1; for (n=1, 86, v=sum(i=0, mx, bitand(i, n)==0); print1(v ", "); mx=max(mx, v))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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