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A334915
Numbers whose XOR-triangles have central zeros.
1
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 16 2020
STATUS
approved