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%I #15 Nov 21 2017 03:12:19
%S 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,
%T 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,
%U 4,4,2,8,4,4,2,4,2,2,1,11,6,6,3,8,4,4
%N a(n) = number of distinct earlier terms that have no common one bit with n in binary representation.
%C This sequence is a variant of A295276: here we count earlier terms without multiplicity, there with multiplicity.
%C The scatterplot of the first terms has fractal features (see scatterplot in Links section); see also A295283 for a variant of this sequence.
%H Rémy Sigrist, <a href="/A295277/b295277.txt">Table of n, a(n) for n = 1..25000</a>
%H Rémy Sigrist, <a href="/A295277/a295277.png">Scatterplot of the first 2^20 terms</a>
%H Rémy Sigrist, <a href="/A295277/a295277_1.png">Colored scatterplot of the first 2^20 terms</a> (where the color is function of min(A000120(a(n)), A000120((Max_{k=1..n-1} a(k))+1-a(n))))
%F a(n) = #{ a(k) such that 0 < k < n and a(k) AND n = 0 } (where AND stands for the bitwise AND operator).
%e The first terms, alongside the distinct earlier terms with no common one bit with n, are:
%e n a(n) Distinct earlier terms with no common one bit with n
%e -- ---- ----------------------------------------------------
%e 1 0 {}
%e 2 1 {0}
%e 3 1 {0}
%e 4 2 {0, 1}
%e 5 2 {0, 2}
%e 6 2 {0, 1}
%e 7 1 {0}
%e 8 3 {0, 1, 2}
%e 9 2 {0, 2}
%e 10 2 {0, 1}
%e 11 1 {0}
%e 12 4 {0, 1, 2, 3}
%e 13 2 {0, 2}
%e 14 2 {0, 1}
%e 15 1 {0}
%e 16 5 {0, 1, 2, 3, 4}
%e 17 3 {0, 2, 4}
%e 18 4 {0, 1, 4, 5}
%e 19 2 {0, 4}
%e 20 4 {0, 1, 2, 3}
%o (PARI) mx=-1; for (n=1, 86, v=sum(i=0, mx, bitand(i,n)==0); print1(v ", "); mx=max(mx,v))
%Y Cf. A000120, A295276, A295283.
%K nonn,base
%O 1,4
%A _Rémy Sigrist_, Nov 19 2017
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