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

1,2

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.

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

Example

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

Prog

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

Crossrefs

Cf. A334769.

Sequence in context: A076769 A105741 A286475 * A308893 A083134 A299143

Adjacent sequences: A334912 A334913 A334914 * A334916 A334917 A334918

Keyword

nonn,base

Author

Rémy Sigrist, May 16 2020

Status

approved