OFFSET
1,2
COMMENTS
Consider a square spiral which begins at the origin and spirals counterclockwise. We define (0, 0) and (1, 0) as the first two nodes. From here, we wish to find the first point along the spiral path which is closer to (0, 0) than to (1, 0). This point would be (0, 1), which is 2 unit lengths away from the previous node. Hence 2 is the first number in our sequence. Likewise, 4 is the next number, as we have to travel 4 unit lengths along the square spiral to reach a point closer to (1, 0) than to (0, 1), and so on.
Based on an empirical observation of the first several terms, I conjecture that lim_{n->infinity} a(n)/n = 8/9.
LINKS
Brian Barsotti, Square Spiral Illustration
Rémy Sigrist, Scatterplot of the first 1000 nodes
Rémy Sigrist, PARI program for A308629
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Brian Barsotti, Jun 11 2019
EXTENSIONS
More terms from Rémy Sigrist, Jun 12 2019
STATUS
approved