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%I #15 Apr 07 2022 10:33:44
%S 0,1,2,1,4,2,3,7,3,4,5,5,6,3,14,3,8,10,8,4,11,5,12,5,11,5,14,3,28,7,8,
%T 18,8,8,18,8,9,21,5,26,5,21,9,11,11,11,25,6,15,49,7,16,29,8,16,31,8,
%U 17,33,14,14,15,16,16,16,15,15,18,8,40,9,18,21,11
%N a(n) is the number of numbers k < n such that A109812(k) AND A109812(n) = 0 (where AND denotes the bitwise AND operator).
%C The magnitude of a(n) is related to A352884(n), the Hamming weight of A109812(n) (see illustration in Links section).
%H Rémy Sigrist, <a href="/A352791/b352791.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A352791/a352791.png">Colored logarithmic scatterplot of the first 100000 terms</a> (where the color is function of the Hamming weight of A109812(n))
%H Rémy Sigrist, <a href="/A352791/a352791.txt">C++ program</a>
%F a(n) <= n-1 with equality iff A109812(n) is a power of 2.
%e The first terms, alongside the binary expansion of A109812(n) and the corresponding k's, are:
%e n a(n) bin(b(n)) k's
%e -- ---- --------- -----------------------------------------------
%e 1 0 1 []
%e 2 1 10 [1]
%e 3 2 100 [1, 2]
%e 4 1 11 [3]
%e 5 4 1000 [1, 2, 3, 4]
%e 6 2 101 [2, 5]
%e 7 3 1010 [1, 3, 6]
%e 8 7 10000 [1, 2, 3, 4, 5, 6, 7]
%e 9 3 110 [1, 5, 8]
%e 10 4 1001 [2, 3, 8, 9]
%e 11 5 10010 [1, 3, 5, 6, 10]
%e 12 5 1100 [1, 2, 4, 8, 11]
%e 13 6 10001 [2, 3, 5, 7, 9, 12]
%e 14 3 1110 [1, 8, 13]
%e 15 14 100000 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
%e 16 3 111 [5, 8, 15]
%o (C++) See Links section.
%Y Cf. A109812, A352884.
%K nonn,base
%O 1,3
%A _Rémy Sigrist_, Apr 03 2022
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