Eduardo J. Acuña Tarazona - cp's OEIS frontend

User: Eduardo J. Acuña Tarazona

Eduardo J. Acuña Tarazona has authored 1 sequences.

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

Eduardo J. Acuña Tarazona, Dec 22 2021

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

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

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

Cf. A181762, A344583.

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 *)

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

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

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User: Eduardo J. Acuña Tarazona

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

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