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).

0, 0, 12, 4, 128, 384, 3404, 740, 37056, 127296, 794316, 286532, 8510656, 25560896, 224057484, 42076324, 2446214016, 8430013568, 51732969356, 18062215300, 553213409792, 1655549411840, 14630859361996, 3227756349540, 159219183713088, 546944274202816, 3411332163636556, 1231354981057220, 36554500089286208, 109782277571646400, 962314238681316620

Offset

0,3

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 binary expansion of n

Index entries for sequences related to cellular automata

Index entries for sequences operating on GF(2)[X]-polynomials

Formula

a(n) = A038184(n) XOR A110240(n).

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

Prog

(PARI)
A048727(n) = bitxor(n, bitxor(2*n, 4*n)); \\ From A048727
A038184(n) = if(!n, 1, A048727(A038184(n-1)));
A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.
A110240(n) = if(!n, 1, A269160(A110240(n-1)));
A327972(n) = bitxor(A038184(n), A110240(n));
\\ Use this one for writing b-files:
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)); };
(Python)
def A048727(n): return(n^(n<<1)^(n<<2))
def A269160(n): return(n^((n<<1)|(n<<2)))
def genA327972():
    '''Yield successive terms of A327972.'''
    s1 = 1
    s2 = 1
    while True:
       yield (s1^s2)
       s1 = A269160(s1)
       s2 = A048727(s2)

Crossrefs

Cf. A003987, A038184, A048727, A110240, A269160.

Cf. also A327971, A327973, A327976, A328103, A328104 for other such combinations.

Sequence in context: A092237 A367323 A081987 * A047709 A002911 A038330

Adjacent sequences: A327969 A327970 A327971 * A327973 A327974 A327975

Keyword

nonn

Author

Antti Karttunen, Oct 03 2019

Status

approved