A350044 Loop starting at 187 in the Collatz-like map {x -> 3x+5 if x is odd, x/2 otherwise}.

187, 566, 283, 854, 427, 1286, 643, 1934, 967, 2906, 1453, 4364, 2182, 1091, 3278, 1639, 4922, 2461, 7388, 3694, 1847, 5546, 2773, 8324, 4162, 2081, 6248, 3124, 1562, 781, 2348, 1174, 587, 1766, 883, 2654, 1327, 3986, 1993, 5984, 2992, 1496, 748, 374, 187, 566, 283, 854

Offset

1,1

Comments

Repeats every forty-four terms starting at 187. Although other loops exist for the "3x+5" map, including 5 -> 20 -> 10 -> 5 and 19 -> 62 -> 31 -> 98 -> 49 -> 152 -> 76 -> 38 -> 19, this loop is much longer and does not appear in the trajectories of as many numbers.

If the Collatz conjecture is false, it will most likely fail because of the existence of a long loop.

a(n) never ends with 0 or 5. a(n+4) - a(n) ends with 0 or 5. - Paul Curtz, Dec 29 2021

Links

Table of n, a(n) for n=1..48.

J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arithmetica, LVI (1990), pp. 33-53.

Formula

a(n) = A181762(a(n-1)) for n > 1, with a(1) = 187.

Example

A181762(187) = 3*(187) + 5 = 566; then A181762(566) = 566/2 = 283.

Mathematica

a[1] = 187; a[n_] := a[n] = If[OddQ[a[n - 1]], 3*a[n - 1] + 5, a[n - 1]/2]; Array[a, 50] (* Amiram Eldar, Dec 25 2021 *)

Prog

(C++)#include <iostream>
int main() {
    unsigned long number = 187;
    int tries = 0;
    while(number > 1 && tries++ < 50) {
        std::cout << number << ", ";
        if (number % 2 == 0)
            number /= 2;
        else
            number = number * 3 + 5;
        }
}
(Python)
N, alst, f = 48, [187], lambda x: x//2 if x%2 == 0 else 3*x + 5
[alst.append(f(alst[-1])) for _ in range(N)]
print(alst) # Michael S. Branicky, Dec 28 2021

Crossrefs

Cf. A181762, A344583.

Sequence in context: A362630 A308810 A063346 * A241670 A134163 A030536

Adjacent sequences: A350041 A350042 A350043 * A350045 A350046 A350047

Keyword

nonn,easy

Author

Eduardo J. Acuña Tarazona, Dec 22 2021

Status

approved