A330732 a(n) is the smallest number whose odd hailstone sequence has length n (including 1 and itself) and is in descending order.

1, 5, 13, 17, 45, 241, 321, 1713, 9137, 24365, 36033, 173261, 231681, 630033, 1642769, 4380717, 11715629, 31241677, 41655569, 111081517, 148108689, 789913009, 1053217345, 1404289793, 3744772781, 9986060749, 13314747665, 35505993773, 94682650061, 128599099649

Offset: 1

Author

Xiangyu Chen, Dec 28 2019

Keywords

• nonn

Comments

The hailstone (Collatz) sequence of a number is defined by repeated operations of f(x), where f(x)=x/2 if x is even, and f(x)=3x+1 if x is odd. The odd numbers of a number's hailstone sequence are also called its odd hailstone sequence.

The odd hailstone sequence of 45 [45, 17, 13, 5, 1] contains the first five terms of this sequence.

Note that a(n+1) isn't necessarily greater than a(n).

Examples

			Consider a(8): [1713, 1285, 241, 181, 17, 13, 5, 1]; the odd hailstone sequence of 1713 is descending and has length 8. 1713 is the lowest such number.
		

Links

• Kevin P. Thompson, Table of n, a(n) for n = 1..36
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A078719, A092893, A182078.

Programs

Mathematica

With[{s = Array[If[AllTrue[Differences@ #, # < 0 &], Length@ #, 0] &@ Select[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, #, # > 1 &], OddQ] &, 10^5]}, Array[FirstPosition[s, #][[1]] &, Max@ s]] (* Michael De Vlieger, Jan 01 2020 *)

PARI

is(k, n) = {my(x=k, v=List([])); while(x>1, if(x%2==0, x=x/2, listput(v, x); x=3*x+1)); 1+#v==n&&v==vecsort(v, , 4); }
a(n) = {k=1; while(is(k, n)==0, k+=2); k; } \\ Jinyuan Wang, Dec 31 2019

Extensions

a(23)-a(30) from Kevin P. Thompson, Jul 23 2022