OFFSET
0,4
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
Rok Cestnik, Term-referencing tree for 1000 terms.
FORMULA
a(n) ~ (3n)^(1/3) (conjectured).
EXAMPLE
a(1) = a(|0-a(0)^2|)+1 = a(|0-0|)+1 = a(0)+1 = 1.
a(2) = a(|1-a(1)^2|)+1 = a(|1-1|)+1 = a(0)+1 = 1.
a(3) = a(|2-a(2)^2|)+1 = a(|2-1|)+1 = a(1)+1 = 2.
a(4) = a(|3-a(3)^2|)+1 = a(|3-4|)+1 = a(1)+1 = 2.
a(5) = a(|4-a(4)^2|)+1 = a(|4-4|)+1 = a(0)+1 = 1.
MATHEMATICA
a[0] = 0; a[n_] := a[n] = a[Abs[n - 1 - a[n - 1]^2]] + 1; Array[a, 100, 0] (* Amiram Eldar, Jul 13 2023 *)
PROG
(Python)
a = [0]; [a.append(a[abs(n-a[n]**2)]+1) for n in range(100)]
CROSSREFS
KEYWORD
nonn
AUTHOR
Rok Cestnik, Jul 13 2023
STATUS
approved