A353220 a(n) is the result of n applications of the function f to n, where f(x) = floor((3*x + 1)/2) (A007494).

0, 2, 5, 12, 21, 41, 72, 134, 210, 365, 608, 1020, 1598, 2624, 4163, 6926, 10598, 17433, 27309, 43605, 67251, 106709, 168128, 266268, 407438, 646460, 1005309, 1574802, 2421374, 3771756, 5817104, 9186359, 13845149, 21814001, 33426338, 51821027, 79295427

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Formula

a(n) = f^n(n) where f(n) = floor((3*n + 1)/2) = A007494(n).

Example

a(0) = f^0 (0) = 0 (f not applied at all);
a(1) = f^1 (1) = f(1) = floor((3*1 + 1)/2) = 2;
a(2) = f^2 (2) = f(f(2)) = floor((3*f(2) + 1)/2) = floor((3*floor((3*2 + 1)/2) + 1)/2) = 5.

Maple

a:= n-> (f-> (f@@n)(n))(t-> floor((3*t+1)/2)):
seq(a(n), n=0..50);  # Alois P. Heinz, May 01 2022

Prog

(C++)
#include <iostream>
using namespace std;
unsigned int f(unsigned int n) {
    return (3*n + 1)/2;
}
unsigned int a(unsigned int pow, unsigned int n) {
    if (pow == 0) return n;
    else return a(pow-1, f(n));
}
int main() {
    for (unsigned int n(0); n <= 20; ++n)
        cout << a(n, n) << " ";
    return 0;
}
(Python)
def f(n):
    return (3*n + 1)//2;
def a(pow, n):
    if (pow == 0): return n;
    else: return a(pow-1, f(n));
l = [a(n, n) for n in range(21)];
(OCaml)
let rec a power n =
  let f n =
    (3*n + 1)/2
  in
  if (power = 0) then n
  else a (power-1) (f n)
;;
for n = 0 to 20 do
  print_string (string_of_int (a n n) ^ " ")
done
(Python)
from functools import reduce
def A353220(n): return reduce(lambda x, _ : (3*x+1)//2, range(n), n) # Chai Wah Wu, May 07 2022

Crossrefs

Cf. A007494 (step), A061419, A353215.

Sequence in context: A182993 A238741 A218904 * A170927 A182201 A106331

Adjacent sequences: A353217 A353218 A353219 * A353221 A353222 A353223

Keyword

nonn

Author

Yves Daaboul, May 01 2022

Status

approved