A072122 Numbers with 12 odd integers in their Collatz (or 3x+1) trajectory.

39, 78, 79, 153, 156, 157, 158, 305, 306, 307, 312, 314, 315, 316, 317, 610, 611, 612, 613, 614, 624, 628, 629, 630, 631, 632, 634, 647, 683, 687, 1220, 1221, 1222, 1224, 1226, 1228, 1229, 1241, 1248, 1256, 1257, 1258, 1260, 1261, 1262, 1264, 1265, 1268

Offset: 1

Author

Jim Nastos, Jun 19 2002

Keywords

• easy
• nonn

Comments

The Collatz (or 3x+1) function is f(x) = x/2 if x is even, 3x+1 if x is odd. The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached.

Examples

			trajectory: 39, 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 has 12 odd numbers.
		

References

• J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A062052-A062060.

Column k=12 of A354236.

Programs

Mathematica

odd12Q[n_]:=Count[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&], ?OddQ]==12; Select[Range[1300],odd12Q] (* _Harvey P. Dale, Oct 17 2011 *)