A327976 Bitwise XOR of trajectories (centrally aligned) of rule 30, and its mirror image, rule 86, when both are started from a lone 1-bit, with the latter delayed by one step: a(n) = A110240(n) XOR 2*A265281(n-1).

5, 23, 73, 359, 1233, 6143, 19225, 93495, 325729, 1518895, 4833289, 23453735, 81443089, 398815039, 1271974489, 6168932215, 21231239841, 99197620591, 314863189193, 1541326542823, 5312985402193, 26258203294847, 82884499362201, 400683454289591, 1406328980294113, 6532877164215983, 20744329255918985, 100303645024039591

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..1024

Antti Karttunen, Terms a(1)-a(256) drawn as binary strings, with 1 bit = 3x3 pixels resolution

Antti Karttunen, Terms a(1)-a(1024) drawn as binary strings, with 1 bit = 1 pixel resolution

Index entries for sequences related to cellular automata

Formula

a(n) = A110240(n) XOR 2*A265281(n-1) = A110240(n) XOR 2*A030101(A110240(n-1)).

Prog

(PARI)
A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.
A110240(n) = if(!n, 1, A269160(A110240(n-1)));
A327973(n) = bitxor(A110240(n), 2*A110240(n-1));
A269161(n) = bitxor(4*n, bitor(2*n, n));
A265281(n) = if(!n, 1, A269161(A265281(n-1)));
A327976(n) = bitxor(A110240(n), 2*A265281(n-1));
\\ Use this one for writing b-files:
A030101(n) = if(n<1, 0, subst(Polrev(binary(n)), x, 2));
A327976write(up_to) = { my(s=1, t, n=0); for(n=1, up_to, t = A269160(s); write("b327976.txt", n, " ", bitxor(2*A030101(s), t)); s = t); };
(Python)
def A269160(n): return(n^((n<<1)|(n<<2)))
def A269161(n): return((n<<2)^((n<<1)|n))
def genA327976():
    '''Yield successive terms of A327976.'''
    s1 = 1
    s2 = 1
    while True:
       s1 = A269160(s1)
       yield (s1^(s2<<1))
       s2 = A269161(s2)

Crossrefs

Cf. A110240, A265281, A269160, A269161, A030101, A327974 (gives the middle bit), A328108 (binary weight).

Cf. also A327971, A327972, A327973, A328103, A328104 for other such combinations.

Sequence in context: A138905 A125955 A103478 * A121868 A111584 A225266

Adjacent sequences: A327973 A327974 A327975 * A327977 A327978 A327979

Keyword

nonn

Author

Antti Karttunen, Oct 04 2019

Status

approved