cp's OEIS Frontend

A328109 Binary weight of A328103: a(n) = A000120(A110240(n) XOR A267357(n)).

%I A328109 #5 Oct 05 2019 18:21:55
%S A328109 0,1,4,3,5,6,8,10,9,11,11,14,14,13,16,11,18,16,17,25,18,21,25,24,22,
%T A328109 30,25,28,30,26,33,34,36,34,33,37,37,44,38,44,51,38,43,48,45,57,38,47,
%U A328109 50,52,49,61,53,56,63,58,56,54,60,59,64,54,60,66,69,60,67,69,72,68,75,74,77,68,78,76,75,78,72,81,80,91,78
%N A328109 Binary weight of A328103: a(n) = A000120(A110240(n) XOR A267357(n)).
%H A328109 Antti Karttunen, <a href="/A328109/b328109.txt">Table of n, a(n) for n = 0..16383</a>
%H A328109 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A328109 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A328109 a(n) = A000120(A328103(n)) = A000120(A110240(n) XOR A267357(n)).
%o A328109 (PARI)
%o A328109 A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.
%o A328109 A110240(n) = if(!n,1,A269160(A110240(n-1)));
%o A328109 A269174(n) = bitand(bitor(n,n<<1),bitor(bitxor(n,n<<1),bitxor(n,n<<2)));
%o A328109 A267357(n) = if(!n,1,A269174(A267357(n-1)));
%o A328109 A328109(n) = hammingweight(bitxor(A110240(n),A267357(n)));
%o A328109 \\ Use this one for writing b-files:
%o A328109 A328109write(up_to) = { my(s1=1, s2=1); for(n=0,up_to, write("b328109.txt", n, " ", hammingweight(bitxor(s1, s2))); s1 = A269160(s1); s2 = A269174(s2)); };
%Y A328109 Cf. A000120, A110240, A267357, A328103.
%Y A328109 Cf. also A328105, A328106, A328107, A328108.
%K A328109 nonn
%O A328109 0,3
%A A328109 _Antti Karttunen_, Oct 05 2019