OFFSET
1,2
COMMENTS
The sequence is growing approximately like sqrt(n). Periods of unrest are connected (see Formula section) with constant rope.
FORMULA
For n from [4*k^2, 4*k^2 + 2*k], a(n) = 2*k + 1 and k = floor(r^(3/2)), r >= 1.
EXAMPLE
a(1) = 1.
a(2) = a(GCD(1, a(1))) + floor(1/a(1)) + 1 = 1 + 1 + 1 = 3.
a(3) = a(GCD(2, a(2))) + floor(2/a(2)) + 1 = 1 + 0 + 1 = 2.
a(4) = a(GCD(3, a(3))) + floor(3/a(3)) + 1 = 1 + 1 + 1 = 3.
and so on.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Feb 12 2024
STATUS
approved