A334915 - OEIS

%I #18 May 24 2020 14:58:56

%S 0,8,9,14,15,16,17,30,31,32,33,62,63,64,65,66,67,72,73,74,75,84,85,86,

%T 87,92,93,94,95,96,97,98,99,104,105,106,107,116,117,118,119,124,125,

%U 126,127,128,129,130,131,148,149,150,151,168,169,170,171,188,189

%N Numbers whose XOR-triangles have central zeros.

%C Depending on the binary length of n, the center of the XOR-triangle for n consists of a single cell or a 2 X 2 X 2 triangle pointing upwards or downwards.

%H Rémy Sigrist, <a href="/A334915/b334915.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A334915/a334915.png">Triangle illustrating the initial terms</a> (central 0's are rendered in yellow)

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/X#XOR-triangles">Index entries for sequences related to XOR-triangles</a>

%e The XOR-triangles for a(8) = 30 and a(18) = 72 are as follows:

%e .   1   1   1   1   0         1   0   0   1   0   0   0

%e .       ---------

%e .     0 \ 0   0 / 1             1   0   1   1   0   0

%e .        \     /                         / \

%e .       0 \ 0 / 1                 1   1 / 0 \ 1   0

%e .          \ /                          -----

%e .         0   1                     0   1   1   1

%e .

%e .           1                         1   0   0

%e .

%e .                                       1   0

%e .

%e .                                         1

%o (PARI) is(n) = {

%o     my (h=#binary(n)-1, l=0, m);

%o     while (abs(h-l)>1, n=bitxor(m=n, n\2); h-=2; l++);

%o     if (h>l, bittest(n,h)==0 && bittest(n,l)==0,

%o         h<l, bittest(n,h)==0 && bittest(n,l)==0 && bittest(m,l)==0,

%o              bittest(n,h)==0

%o     )

%o }

%Y Cf. A334769.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, May 16 2020