A328103 - OEIS

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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).

9

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

(list; graph; refs; listen; history; text; internal format)

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