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).

0, 4, 30, 100, 398, 1748, 6510, 28628, 102590, 456132, 1642078, 7289764, 26336590, 116802708, 420215854, 1865678868, 6741198206, 29904470916, 107568473246, 477629808612, 1725756768270, 7655529847380, 27537572248046, 122273029571156, 441793665700414, 1959816793456452, 7049616389341662, 31301899019407908, 113099196716630990, 501713069953322004

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..1023

Antti Karttunen, Terms up to a(255) drawn as binary strings, with 1 bit = 3x3 pixels resolution

Antti Karttunen, Terms up to a(1023) drawn as binary strings, with 1 bit = 1 pixel resolution

Index entries for sequences related to cellular automata

Formula

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

Prog

(PARI)
A269160(n) = bitxor(n, bitor(2*n, 4*n));
A110240(n) = if(!n, 1, A269160(A110240(n-1)));
A269174(n) = bitand(bitor(n, n<<1), bitor(bitxor(n, n<<1), bitxor(n, n<<2)));
A267357(n) = if(!n, 1, A269174(A267357(n-1)));
A328103(n) = bitxor(A110240(n), A267357(n));
\\ Use this one for writing b-files:
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)); };
(Python)
def A269160(n): return(n^((n<<1)|(n<<2)))
def A269174(n): return((n|(n<<1))&((n^(n<<1))|(n^(n<<2))))
def genA328103():
    '''Yield successive terms of A328103.'''
    s1 = 1
    s2 = 1
    while True:
       yield (s1^s2)
       s1 = A269174(s1)
       s2 = A269160(s2)

Crossrefs

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

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

Sequence in context: A201975 A109670 A014697 * A211624 A027297 A211628

Adjacent sequences: A328100 A328101 A328102 * A328104 A328105 A328106

Keyword

nonn

Author

Antti Karttunen, Oct 05 2019

Status

approved