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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.

%I A375265 #17 Aug 16 2024 04:27:52
%S A375265 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,
%T A375265 88,10,94,16,11,17,106,12,112,19,13,20,124,14,130,22,15,23,142,16,148,
%U A375265 25,17,26,160,18,166,28,19,29,178,20,184,31,21,32,196,22,202,34,23
%N 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.
%C A375265 Anderson (1987) reformulates the 3x+1 conjecture using this function.
%H A375265 Paolo Xausa, <a href="/A375265/b375265.txt">Table of n, a(n) for n = 1..10000</a>
%H A375265 Stuart Anderson, <a href="https://doi.org/10.2307/3617045">Struggling with the 3x+1 problem</a>, The Mathematical Gazette, Vol. 71, Issue 458, December 1987, p. 273 (see A005186 for a scanned copy).
%H A375265 Jeffrey C. Lagarias, <a href="https://doi.org/10.48550/arXiv.math/0309224">The 3x + 1 Problem: An Annotated Bibliography (1963-1999)</a>, arXiv:math/0309224 [math.NT], 2011, p. 6.
%H A375265 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>.
%H A375265 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,2,0,0,0,0,0,-1).
%p A375265 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
%t A375265 A375265[n_] := Which[Divisible[n, 3], n/3, Divisible[n, 2], n/2, True,3*n + 1];
%t A375265 Array[A375265, 100]
%Y A375265 Cf. A375266 (trajectories).
%Y A375265 Cf. A005186, A006370, A014682, A185452, A349407, A350515.
%K A375265 nonn,easy
%O A375265 1,1
%A A375265 _Paolo Xausa_, Aug 08 2024