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A324245 The modified Collatz map considered by Vaillant and Delarue.

%I A324245 #39 Aug 10 2023 13:13:05
%S A324245 0,2,0,5,3,8,1,11,6,14,2,17,9,20,3,23,12,26,4,29,15,32,5,35,18,38,6,
%T A324245 41,21,44,7,47,24,50,8,53,27,56,9,59,30,62,10,65,33,68,11,71,36,74,12,
%U A324245 77,39,80,13,83,42,86,14,89,45,92,15,95,48,98,16,101,51,104,17,107,54,110,18,113,57,116,19,119,60
%N A324245 The modified Collatz map considered by Vaillant and Delarue.
%C A324245 This is a modified Collatz-Terras map (A060322), called in the Vaillant and Delarue link f.
%C A324245 The Collatz conjecture: iterations of the map f = a: N_0 -> N_0 with n -> a(n) lead always to 0.
%C A324245 The minimal number k with a^{[k]}(n) = 0 is given by A324037(n).
%C A324245 The tree CfTree, related to this map, giving the branches which lead to 0 for each vertex label of level n >= 0 is given in A324246.
%H A324245 Antti Karttunen, <a href="/A324245/b324245.txt">Table of n, a(n) for n = 0..20000</a>
%H A324245 Nicolas Vaillant and Philippe Delarue, <a href="https://web.archive.org/web/20220317020641/http://nini-software.fr/site/uploads/arithmetics/collatz/Intrinsic%203x+1%20V2.01.pdf">The hidden face of the 3x+1 problem. Part I: Intrinsic algorithm</a>, April 26 2019.
%H A324245 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A324245 a(n) = (3*n+1)/2 if n is odd, 3*n/4 if n == 0 (mod 4), and (n-2)/4 if n == 2 (mod 4).
%F A324245 a(n) = A349414(n) + n. - _Ruud H.G. van Tol_, Dec 08 2021
%F A324245 G.f.: x*(2 + 5*x^2 + 3*x^3 + 4*x^4 + x^5 + x^6)/(1 - x^4)^2. - _Stefano Spezia_, Dec 08 2021
%t A324245 a[n_]:=If[OddQ@n,(3n+1)/2,If[Mod[n,4]==0,3n/4,(n-2)/4]];Array[a,51,0] (* _Giorgos Kalogeropoulos_, Dec 08 2021 *)
%o A324245 (PARI) A324245(n) = if(n%2, (1+3*n)/2, if(!(n%4), 3*(n/4), (n-2)/4)); \\ (After Mathematica-code) - _Antti Karttunen_, Dec 09 2021
%Y A324245 Cf. A060322, A324037, A324246, A349414.
%K A324245 nonn,easy
%O A324245 0,2
%A A324245 _Nicolas Vaillant_, Philippe Delarue, _Wolfdieter Lang_, May 09 2019
%E A324245 More terms from _Antti Karttunen_, Dec 09 2021