%I #12 Oct 05 2019 18:21:09

%S 0,4,30,100,398,1748,6510,28628,102590,456132,1642078,7289764,

%T 26336590,116802708,420215854,1865678868,6741198206,29904470916,

%U 107568473246,477629808612,1725756768270,7655529847380,27537572248046,122273029571156,441793665700414,1959816793456452,7049616389341662,31301899019407908,113099196716630990,501713069953322004

%N 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 Antti Karttunen, <a href="/A328103/b328103.txt">Table of n, a(n) for n = 0..1023</a>

%H Antti Karttunen, <a href="/A328103/a328103.png">Terms up to a(255) drawn as binary strings, with 1 bit = 3x3 pixels resolution</a>

%H 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 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%F a(n) = A110240(n) XOR A267357(n), where XOR is bitwise exclusive or (A003987).

%o (PARI)

%o A269160(n) = bitxor(n, bitor(2*n, 4*n));

%o A110240(n) = if(!n,1,A269160(A110240(n-1)));

%o A269174(n) = bitand(bitor(n,n<<1),bitor(bitxor(n,n<<1),bitxor(n,n<<2)));

%o A267357(n) = if(!n,1,A269174(A267357(n-1)));

%o A328103(n) = bitxor(A110240(n),A267357(n));

%o \\ Use this one for writing b-files:

%o 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 (Python)

%o def A269160(n): return(n^((n<<1)|(n<<2)))

%o def A269174(n): return((n|(n<<1))&((n^(n<<1))|(n^(n<<2))))

%o def genA328103():

%o '''Yield successive terms of A328103.'''

%o s1 = 1

%o s2 = 1

%o while True:

%o yield (s1^s2)

%o s1 = A269174(s1)

%o s2 = A269160(s2)

%Y Cf. A003987, A110240, A267357, A269160, A269174, A328109 (binary weight of terms).

%Y Cf. also A327971, A327972, A327973, A327976, A328104 for other such combinations, and also A328111.

%K nonn

%O 0,2

%A _Antti Karttunen_, Oct 05 2019