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

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