A181762 -id:A181762 - cp's OEIS frontend

A187486 Distance between first and second positions of A181762(n).

0, 15, 0, 25, 0, 35, 0, 45, 0, 55, 0, 65, 0, 75, 0, 85, 15, 95, 0, 105, 0, 115, 0, 125, 0, 135, 0, 145, 25, 155, 0, 165, 0, 175, 0, 185, 0, 195, 0, 205, 35, 215, 0, 225, 0, 235, 0, 245, 0, 255, 0, 265, 45, 275, 0, 285, 0, 295, 0, 305, 0, 315, 0, 325, 55, 335, 0, 345, 0, 355

Offset: 0

Zak Seidov, Mar 10 2011

nonn

Some entries of A181762 occur twice some only once.
The sequence gives the distance between first and second positions of A181762(n),
a(n)=0 if A181762(n) occurs only once.
The numbers that occur in A181762 only once are 0, 2, 4, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 30, 32, 34, 36, 38, 42, 44, 46, ...

Cf. A181762.

A330710 Numbers that reach 1 in the 3x + 5 variation of Collatz map.

Original entry on oeis.org

1, 2, 4, 8, 9, 16, 18, 32, 36, 41, 53, 64, 69, 72, 82, 106, 107, 111, 128, 138, 141, 143, 144, 163, 164, 169, 189, 212, 214, 217, 219, 222, 231, 247, 256, 263, 276, 281, 282, 286, 287, 288, 299, 326, 328, 331, 338, 349, 363, 373, 378, 381, 383, 397

Offset: 1

Cara Bennett, Dec 27 2019

nonn

In this variation of the Collatz function, f(x) = x/2 if x is even, 3x + 5 if x is odd.
f(a(n)) will end in the loop 8, 4, 2, 1.
For any odd number n in the sequence, n*2^x where x is a positive integer will also be in the sequence.

			For n = 53, the numbers produced are 53 -> 164 -> 82 -> 41 -> 128 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1 -> 8 -> 4 -> 2 -> 1 -> ...

Cf. A000079, A181762.

Select[Range@ 400, Function[n, NestWhile[If[EvenQ@ #, #/2, 3 # + 5] &, n, And[FreeQ[{##}, 1], Count[{##}, n] <= 2] &, All, 120] == 1]] (* Michael De Vlieger, Dec 27 2019 *)

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

Original entry on oeis.org

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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A187486 Distance between first and second positions of A181762(n).

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A330710 Numbers that reach 1 in the 3x + 5 variation of Collatz map.

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

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