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Number of steps needed to reach 4,2,1 in Collatz' 3*n+1 conjecture.
8

%I #16 Aug 10 2022 10:07:28

%S 1,2,5,0,3,6,14,1,17,4,12,7,7,15,15,2,10,18,18,5,5,13,13,8,21,8,109,

%T 16,16,16,104,3,24,11,11,19,19,19,32,6,107,6,27,14,14,14,102,9,22,22,

%U 22,9,9,110,110,17,30,17,30,17,17,105,105,4,25,25,25,12,12,12

%N Number of steps needed to reach 4,2,1 in Collatz' 3*n+1 conjecture.

%C a(n) = number of iterations of the Collatz 3*x+1 map applied to n until the conjectured 4,2,1 sequence is reached.

%D C. A. Pickover, Dr. Googols wundersame Welt der Zahlen, Deutscher Taschenbuch Verlag, Kap. 14, pp. 87, 193. German translation of: Wonders of numbers - Adventures in Mathematics, Mind and Meaning, Oxford University Press 2003.

%H Ken Conrow, <a href="https://web.archive.org/web/20170829042515/http://www-personal.ksu.edu:80/~kconrow/">Collatz 3n+1 Problem.</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F a(n) = A006577(n) - 2, n >= 3, a(1)=1, a(2)=2.

%e a(1)=1 because the sequence for n=1 is 1,4,2,1.

%e a(4)=0 from 4,2,1.

%e a(7)=14 from 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.

%t f[n_] := If[EvenQ[n], n/2, 3 n + 1];

%t a[n_] := Length[NestWhileList[f, n, {#1, #2, #3} != {4, 2, 1}&, 3]] - 3;

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Aug 08 2022 *)

%Y Essentially the same sequence as A139399.

%Y Cf. A006370, A006577.

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, Oct 31 2005