cp's OEIS Frontend

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

%I A330732 #30 Nov 25 2022 12:46:42
%S A330732 1,5,13,17,45,241,321,1713,9137,24365,36033,173261,231681,630033,
%T A330732 1642769,4380717,11715629,31241677,41655569,111081517,148108689,
%U A330732 789913009,1053217345,1404289793,3744772781,9986060749,13314747665,35505993773,94682650061,128599099649
%N A330732 a(n) is the smallest number whose odd hailstone sequence has length n (including 1 and itself) and is in descending order.
%C A330732 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.
%C A330732 The odd hailstone sequence of 45 [45, 17, 13, 5, 1] contains the first five terms of this sequence.
%C A330732 Note that a(n+1) isn't necessarily greater than a(n).
%H A330732 Kevin P. Thompson, <a href="/A330732/b330732.txt">Table of n, a(n) for n = 1..36</a>
%H A330732 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A330732 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.
%t A330732 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 *)
%o A330732 (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); }
%o A330732 a(n) = {k=1; while(is(k, n)==0, k+=2); k; } \\ _Jinyuan Wang_, Dec 31 2019
%Y A330732 Cf. A078719, A092893, A182078.
%K A330732 nonn
%O A330732 1,2
%A A330732 _Xiangyu Chen_, Dec 28 2019
%E A330732 a(23)-a(30) from _Kevin P. Thompson_, Jul 23 2022