cp's OEIS Frontend

A328105 Binary weight of A328104: a(n) = A000120(A110240(n) OR 2*A110240(n)).

%I A328105 #11 Oct 05 2019 18:21:23
%S A328105 2,4,5,8,7,12,9,15,11,17,17,20,19,26,21,29,22,27,30,33,30,34,37,40,37,
%T A328105 39,41,49,44,49,48,53,41,56,49,64,50,62,59,66,64,60,66,69,61,77,65,73,
%U A328105 67,74,70,89,78,87,78,94,85,88,89,100,91,101,95,110,92,85,98,102,102,102,115,109,101,105,121,118,121,129
%N A328105 Binary weight of A328104: a(n) = A000120(A110240(n) OR 2*A110240(n)).
%H A328105 Antti Karttunen, <a href="/A328105/b328105.txt">Table of n, a(n) for n = 0..16383</a>
%H A328105 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A328105 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A328105 a(n) = A000120(A328104(n)) = A000120(A163617(A110240(n))).
%F A328105 For all n >= 0, A070952(a) < a(n) <= 2*A070952(n).
%o A328105 (PARI)
%o A328105 A269160(n) = bitxor(n, bitor(2*n, 4*n));
%o A328105 A110240(n) = if(!n,1,A269160(A110240(n-1)));
%o A328105 A163617(n) = bitor(n,n<<1);
%o A328105 A328105(n) = hammingweight(A163617(A110240(n)));
%o A328105 \\ Use this one for writing b-files:
%o A328105 A328105write(up_to) = { my(s=1, n=0); for(n=0,up_to, write("b328105.txt", n, " ", hammingweight(bitor(s, s<<1))); s = A269160(s)); };
%Y A328105 Cf. A000120, A110240, A163617, A269160, A328104.
%Y A328105 Cf. also A070952, A328106, A328107, A328108, A328109.
%K A328105 nonn
%O A328105 0,1
%A A328105 _Antti Karttunen_, Oct 05 2019