OFFSET
1,12
COMMENTS
As the terms are not distinct the first two numbers of any new row or column will always be zero. In the first 500000 terms the last zero that is not at the beginning of a row or column is a(190) = 0. Is it unknown if more such zeros exist. In the same range the smallest positive numbers not yet occurring are 5, 9, 11, 12, 15, 19, 20, ... . It is unknown if all integers eventually appear. The terms increase rapidly in size; in the first 500000 terms the largest positive term is a(499848) = 1267...5398, a number with 226 digits.
LINKS
Scott R. Shannon, Table of n, a(n) for n = 1..10000.
Scott R. Shannon, Image of log_10(a(n)+1) of the absolute value of the first 500000 terms.
Scott R. Shannon, Image showing the sign of the first 500000 terms on the spiral. White is positive, black is negative, yellow is zero.
EXAMPLE
The spiral begins:
. .
. |
0__-3___2__-2___3___0___0 -7
| | |
0 0__-2___1___0___0 -3 4
| | | | |
3 0 0___0___0 -2 2 0
| | | | | | |
-1 0 0 1___0 0 -1 4
| | | | | |
-1 -1 0___0___1___0 0 -5
| | | |
1 0___0___0__-2___2___0 0
| |
0___0___1___0___0__-5___8___0
.
.
a(9) = 1 as a(1) = 1 and a(2)..a(8) = 0, therefore a(9) = 1 so the sum of the eight numbers around a(1) equals 1.
a(12) = -2 as a(2) = 0 while a(1), a(9) = 1, a(2)..a(4), a(8), a(10), a(11) = 0, therefore a(12) = -2 so the sum of the eight numbers around a(1) equals 0.
CROSSREFS
KEYWORD
sign
AUTHOR
Scott R. Shannon, Jun 14 2023
STATUS
approved