|
| |
|
|
A364801
|
|
The number of iterations that n requires to reach a fixed point under the map x -> A022290(x).
|
|
3
|
|
|
|
0, 0, 0, 0, 1, 2, 3, 4, 3, 4, 5, 4, 4, 5, 6, 5, 4, 5, 6, 5, 5, 5, 6, 7, 6, 7, 6, 5, 5, 6, 7, 6, 6, 7, 6, 5, 5, 6, 7, 6, 7, 6, 6, 6, 6, 7, 8, 7, 6, 7, 8, 7, 7, 8, 7, 6, 7, 6, 6, 7, 7, 8, 7, 7, 6, 7, 8, 7, 7, 8, 7, 6, 7, 6, 6, 7, 7, 8, 7, 7, 7, 8, 7, 7, 7, 8, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
COMMENTS
|
a(n) is well-defined since A022290(n) = n for n <= 3 (the fixed points), and A022290(n) < n for n >= 4.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = a(A022290(n)) + 1, for n >= 4.
|
|
|
EXAMPLE
|
For n = 4 the trajectory is 4 -> 3. The number of iterations is 1, thus a(4) = 1.
For n = 6 the trajectory is 6 -> 5 -> 4 -> 3. The number of iterations is 3, thus a(6) = 3.
|
|
|
MATHEMATICA
|
f[n_] := f[n] = Module[{d = IntegerDigits[n, 2], nd}, nd = Length[d]; Total[d * Fibonacci[Range[nd + 1, 2, -1]]]]; (* A022290 *)
a[n_] := -2 + Length@ FixedPointList[f, n]; Array[a, 100, 0]
|
|
|
PROG
|
(PARI) f(n) = {my(b = binary(n), nb = #b); sum(i = 1, nb, b[i] * fibonacci(nb - i + 2)); } \\ A022290
a(n) = if(n < 4, 0, a(f(n)) + 1);
(Python)
if n<4: return 0
a, b, s = 1, 2, 0
for i in bin(n)[-1:1:-1]:
if int(i):
s += a
a, b = b, a+b
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
