A324245 - OEIS

%I #39 Aug 10 2023 13:13:05

%S 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 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 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 The modified Collatz map considered by Vaillant and Delarue.

%C This is a modified Collatz-Terras map (A060322), called in the Vaillant and Delarue link f.

%C The Collatz conjecture: iterations of the map f = a: N_0 -> N_0 with n -> a(n) lead always to 0.

%C The minimal number k with a^{[k]}(n) = 0 is given by A324037(n).

%C 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 Antti Karttunen, <a href="/A324245/b324245.txt">Table of n, a(n) for n = 0..20000</a>

%H 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 <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 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 a(n) = A349414(n) + n. - _Ruud H.G. van Tol_, Dec 08 2021

%F 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 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 (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 Cf. A060322, A324037, A324246, A349414.

%K nonn,easy

%O 0,2

%A _Nicolas Vaillant_, Philippe Delarue, _Wolfdieter Lang_, May 09 2019

%E More terms from _Antti Karttunen_, Dec 09 2021