OFFSET
1,2
COMMENTS
a(n) = n^2 if and only if A159257(n) = 0.
a(n) >= A075464(n).
If n = 6k-1 for some integer k, then a(n) <= 26k^2 - 12k + 1. This upper bound is equal to a(n) when A159257(n) = 2. Further, it is conjectured that if A159257(n) = 2, then n = 6k-1 for some integer k.
It is conjectured that if A159257(n) = 4, then n = 5k-1 for some integer k, and a(n) = 17k^2 - 10k.
It is conjectured that if A159257(n) = 6, then n = 12k-1 for some integer k, and a(n) = 88k^2 - 24k + 1
It is conjectured that if A159257(n) = 8, then either n = 10k-1 or n = 17k-1 for some integer k. If n = 10k-1, then a(n) = 60k^2 - 20k - 3. If n = 17k-1, then a(n) = 161k^2 - 34k - 3.
It is conjectured that if A159257(n) = 10, then n = 30k-1 for some integer k, and a(n) = 506k^2 - 60k - 3.
239 <= a(23) <= 305.
LINKS
William Boyles, Most Clicks Problem in Lights Out, arXiv:2201.03452 [math.CO], 2022.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
William Boyles, Apr 21 2022
STATUS
approved