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A353292 a(n) is the number of positive integers k <= n that have at least one common 1-bit with n.

%I A353292 #11 Apr 11 2022 16:34:24
%S A353292 0,1,1,3,1,4,5,7,1,6,7,10,9,12,13,15,1,10,11,16,13,18,19,22,17,22,23,
%T A353292 26,25,28,29,31,1,18,19,28,21,30,31,36,25,34,35,40,37,42,43,46,33,42,
%U A353292 43,48,45,50,51,54,49,54,55,58,57,60,61,63,1,34,35,52,37
%N A353292 a(n) is the number of positive integers k <= n that have at least one common 1-bit with n.
%C A353292 See A353293 for the corresponding k's.
%H A353292 Rémy Sigrist, <a href="/A353292/b353292.txt">Table of n, a(n) for n = 0..8192</a>
%H A353292 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A353292 a(n) = n - A115378(n) for any n > 0.
%F A353292 a(n) = A062050(n) + A088512(n) * A080100(n) for any n > 0.
%F A353292 a(2^k) = 1 for any k >= 0.
%F A353292 a(2^k - 1) = 2^k - 1 for any k >= 0.
%e A353292 For n = 10:
%e A353292 - we have:
%e A353292       k   10 AND k
%e A353292       --  --------
%e A353292        1         0
%e A353292        2         2
%e A353292        3         2
%e A353292        4         0
%e A353292        5         0
%e A353292        6         2
%e A353292        7         2
%e A353292        8         8
%e A353292        9         8
%e A353292       10        10
%e A353292 - so a(10) = #{2, 3, 6, 7, 8, 9, 10} = 7.
%o A353292 (PARI) a(n) = { my (h=hammingweight(n), w=#binary(n)); n-2^(w-1)+1 + (2^(h-1)-1)*2^(w-h) }
%Y A353292 Cf. A062050, A080100, A088512, A115378, A353293.
%K A353292 nonn,base
%O A353292 0,4
%A A353292 _Rémy Sigrist_, Apr 09 2022