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A328103 Bitwise XOR of trajectories of rule 30 and rule 124, when both are started from a lone 1 cell: a(n) = A110240(n) XOR A267357(n).

%I A328103 #12 Oct 05 2019 18:21:09
%S A328103 0,4,30,100,398,1748,6510,28628,102590,456132,1642078,7289764,
%T A328103 26336590,116802708,420215854,1865678868,6741198206,29904470916,
%U A328103 107568473246,477629808612,1725756768270,7655529847380,27537572248046,122273029571156,441793665700414,1959816793456452,7049616389341662,31301899019407908,113099196716630990,501713069953322004
%N A328103 Bitwise XOR of trajectories of rule 30 and rule 124, when both are started from a lone 1 cell: a(n) = A110240(n) XOR A267357(n).
%H A328103 Antti Karttunen, <a href="/A328103/b328103.txt">Table of n, a(n) for n = 0..1023</a>
%H A328103 Antti Karttunen, <a href="/A328103/a328103.png">Terms up to a(255) drawn as binary strings, with 1 bit = 3x3 pixels resolution</a>
%H A328103 Antti Karttunen, <a href="/A328103/a328103_1.png">Terms up to a(1023) drawn as binary strings, with 1 bit = 1 pixel resolution</a>
%H A328103 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A328103 a(n) = A110240(n) XOR A267357(n), where XOR is bitwise exclusive or (A003987).
%o A328103 (PARI)
%o A328103 A269160(n) = bitxor(n, bitor(2*n, 4*n));
%o A328103 A110240(n) = if(!n,1,A269160(A110240(n-1)));
%o A328103 A269174(n) = bitand(bitor(n,n<<1),bitor(bitxor(n,n<<1),bitxor(n,n<<2)));
%o A328103 A267357(n) = if(!n,1,A269174(A267357(n-1)));
%o A328103 A328103(n) = bitxor(A110240(n),A267357(n));
%o A328103 \\ Use this one for writing b-files:
%o A328103 A328103write(up_to) = { my(s1=1, s2=1); for(n=0,up_to, write("b328103.txt", n, " ", bitxor(s1, s2)); s1 = A269160(s1); s2 = A269174(s2)); };
%o A328103 (Python)
%o A328103 def A269160(n): return(n^((n<<1)|(n<<2)))
%o A328103 def A269174(n): return((n|(n<<1))&((n^(n<<1))|(n^(n<<2))))
%o A328103 def genA328103():
%o A328103     '''Yield successive terms of A328103.'''
%o A328103     s1 = 1
%o A328103     s2 = 1
%o A328103     while True:
%o A328103        yield (s1^s2)
%o A328103        s1 = A269174(s1)
%o A328103        s2 = A269160(s2)
%Y A328103 Cf. A003987, A110240, A267357, A269160, A269174, A328109 (binary weight of terms).
%Y A328103 Cf. also A327971, A327972, A327973, A327976, A328104 for other such combinations, and also A328111.
%K A328103 nonn
%O A328103 0,2
%A A328103 _Antti Karttunen_, Oct 05 2019