A334915 Numbers whose XOR-triangles have central zeros.

0, 8, 9, 14, 15, 16, 17, 30, 31, 32, 33, 62, 63, 64, 65, 66, 67, 72, 73, 74, 75, 84, 85, 86, 87, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 116, 117, 118, 119, 124, 125, 126, 127, 128, 129, 130, 131, 148, 149, 150, 151, 168, 169, 170, 171, 188, 189

Offset: 1

Author

Rémy Sigrist, May 16 2020

Keywords

• nonn
• base

Comments

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.

Examples

			The XOR-triangles for a(8) = 30 and a(18) = 72 are as follows:
.   1   1   1   1   0         1   0   0   1   0   0   0
.       ---------
.     0 \ 0   0 / 1             1   0   1   1   0   0
.        \     /                         / \
.       0 \ 0 / 1                 1   1 / 0 \ 1   0
.          \ /                          -----
.         0   1                     0   1   1   1
.
.           1                         1   0   0
.
.                                       1   0
.
.                                         1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Triangle illustrating the initial terms (central 0's are rendered in yellow)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to XOR-triangles

Crossrefs

Cf. A334769.

Programs

PARI

is(n) = {
    my (h=#binary(n)-1, l=0, m);
    while (abs(h-l)>1, n=bitxor(m=n, n\2); h-=2; l++);
    if (h>l, bittest(n,h)==0 && bittest(n,l)==0,
        h