A375265 a(n) = n/3 if n mod 3 = 0; otherwise a(n) = n/2 if n mod 2 = 0; otherwise a(n) = 3*n + 1.

4, 1, 1, 2, 16, 2, 22, 4, 3, 5, 34, 4, 40, 7, 5, 8, 52, 6, 58, 10, 7, 11, 70, 8, 76, 13, 9, 14, 88, 10, 94, 16, 11, 17, 106, 12, 112, 19, 13, 20, 124, 14, 130, 22, 15, 23, 142, 16, 148, 25, 17, 26, 160, 18, 166, 28, 19, 29, 178, 20, 184, 31, 21, 32, 196, 22, 202, 34, 23

Offset

1,1

Comments

Anderson (1987) reformulates the 3x+1 conjecture using this function.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Stuart Anderson, Struggling with the 3x+1 problem, The Mathematical Gazette, Vol. 71, Issue 458, December 1987, p. 273 (see A005186 for a scanned copy).

Jeffrey C. Lagarias, The 3x + 1 Problem: An Annotated Bibliography (1963-1999), arXiv:math/0309224 [math.NT], 2011, p. 6.

Index entries for sequences related to 3x+1 (or Collatz) problem.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).

Formula

From Elmo R. Oliveira, May 14 2026: (Start)

a(n) = 2*a(n-6) - a(n-12) for n > 12.

G.f.: x*(4 + x + x^2 + 2*x^3 + 16*x^4 + 2*x^5 + 14*x^6 + 2*x^7 + x^8 + x^9 + 2*x^10) / (1 - x^6)^2. (End)

Maple

a := n -> ifelse(irem(n, 3) = 0, iquo(n, 3), ifelse(irem(n, 2) = 0, iquo(n, 2), 3*n + 1)): seq(a(n), n = 1..69);  # Peter Luschny, Aug 14 2024

Mathematica

A375265[n_] := Which[Divisible[n, 3], n/3, Divisible[n, 2], n/2, True, 3*n + 1];
Array[A375265, 100]

Crossrefs

Cf. A375266 (trajectories).

Cf. A005186, A006370, A014682, A185452, A349407, A350515.

Sequence in context: A355694 A265273 A376985 * A341932 A293770 A111311

Adjacent sequences: A375262 A375263 A375264 * A375266 A375267 A375268

Keyword

nonn,easy

Author

Paolo Xausa, Aug 08 2024

Status

approved