A112695 Number of steps needed to reach 4,2,1 in Collatz' 3*n+1 conjecture.

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, 16, 16, 16, 104, 3, 24, 11, 11, 19, 19, 19, 32, 6, 107, 6, 27, 14, 14, 14, 102, 9, 22, 22, 22, 9, 9, 110, 110, 17, 30, 17, 30, 17, 17, 105, 105, 4, 25, 25, 25, 12, 12, 12

Offset: 1

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• nonn
• easy

Comments

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

Examples

			a(1)=1 because the sequence for n=1 is 1,4,2,1.
a(4)=0 from 4,2,1.
a(7)=14 from 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
		

References

• 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.

Links

• Ken Conrow, Collatz 3n+1 Problem.
• Eric Weisstein's World of Mathematics, Collatz Problem
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Essentially the same sequence as A139399.

Cf. A006370, A006577.

Programs

Mathematica

f[n_] := If[EvenQ[n], n/2, 3 n + 1];
a[n_] := Length[NestWhileList[f, n, {#1, #2, #3} != {4, 2, 1}&, 3]] - 3;
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Aug 08 2022 *)

Formula

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