OFFSET
0
COMMENTS
As all squares are numbered from the difference between square spiral numbers which are either 0 or 1, all terms in the sequence are 0 or 1.
Inspired by Pascal's Spiral A334742.
LINKS
Scott R. Shannon, Image of the spiral for a 101x101 grid. Black squares = 0 and white squares = 1, The central square a(0) = 0 is shown in red for clarity.
Scott R. Shannon, Image of the spiral for a 2001x2001 grid.
EXAMPLE
The spiral begins:
.
--0---1---0---0---1---1
|
1---1---0---1---0 1
| | |
0 1---1---1 0 1
| | | | |
1 1 0---1 1 1
| | | |
0 1---1---0---0 0
| |
0---1---0---0---0---0
.
a(0) = 0; a(1) = 1 by definition.
a(2) = 1 as it only has one adjacent visited square a(1) = 1 so it takes that number.
a(3) = 1 as it has adjacent visited squares a(2) = 1 and a(0) = 0 and the difference between 1 and 0 is 1.
a(7) = 1 as it has adjacent visited squares a(6) = 1 and a(0) = 0 and the difference between 1 and 0 is 1.
a(8) = 0 as it has adjacent visited squares a(7) = 1 and a(1) = 1 and the difference between 1 and 1 is 0.
a(9) = 0 as it only has one adjacent visited square a(8) = 0 so it takes that number.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, May 12 2020
STATUS
approved