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A327972 Bitwise XOR of trajectories of rule 30 and rule 150, when both are started from a lone 1 cell: a(n) = A110240(n) XOR A038184(n).

%I A327972 #38 Mar 07 2023 07:42:37
%S A327972 0,0,12,4,128,384,3404,740,37056,127296,794316,286532,8510656,
%T A327972 25560896,224057484,42076324,2446214016,8430013568,51732969356,
%U A327972 18062215300,553213409792,1655549411840,14630859361996,3227756349540,159219183713088,546944274202816,3411332163636556,1231354981057220,36554500089286208,109782277571646400,962314238681316620
%N A327972 Bitwise XOR of trajectories of rule 30 and rule 150, when both are started from a lone 1 cell: a(n) = A110240(n) XOR A038184(n).
%H A327972 Antti Karttunen, <a href="/A327972/b327972.txt">Table of n, a(n) for n = 0..1023</a>
%H A327972 Antti Karttunen, <a href="/A327972/a327972.png">Terms up to a(255) drawn as binary strings, with 1 bit = 3x3 pixels resolution</a>
%H A327972 Antti Karttunen, <a href="/A327972/a327972_1.png">Terms up to a(1023) drawn as binary strings, with 1 bit = 1 pixel resolution</a>
%H A327972 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A327972 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A327972 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F A327972 a(n) = A038184(n) XOR A110240(n).
%F A327972 Conjecture: for n > 1, floor(log_2(a(n))) = 2*n - (1,2,1,4,1,2,1,5 according as n == 0..7 (mod 8), respectively). - _Alan Michael Gómez Calderón_, Mar 02 2023
%o A327972 (PARI)
%o A327972 A048727(n) = bitxor(n, bitxor(2*n, 4*n)); \\ From A048727
%o A327972 A038184(n) = if(!n,1,A048727(A038184(n-1)));
%o A327972 A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.
%o A327972 A110240(n) = if(!n,1,A269160(A110240(n-1)));
%o A327972 A327972(n) = bitxor(A038184(n), A110240(n));
%o A327972 \\ Use this one for writing b-files:
%o A327972 A327972write(up_to) = { my(s1=1, s2=1); for(n=0,up_to, write("b327972.txt", n, " ", bitxor(s1, s2)); s1 = A048727(s1); s2 = A269160(s2)); };
%o A327972 (Python)
%o A327972 def A048727(n): return(n^(n<<1)^(n<<2))
%o A327972 def A269160(n): return(n^((n<<1)|(n<<2)))
%o A327972 def genA327972():
%o A327972     '''Yield successive terms of A327972.'''
%o A327972     s1 = 1
%o A327972     s2 = 1
%o A327972     while True:
%o A327972        yield (s1^s2)
%o A327972        s1 = A269160(s1)
%o A327972        s2 = A048727(s2)
%Y A327972 Cf. A003987, A038184, A048727, A110240, A269160.
%Y A327972 Cf. also A327971, A327973, A327976, A328103, A328104 for other such combinations.
%K A327972 nonn
%O A327972 0,3
%A A327972 _Antti Karttunen_, Oct 03 2019