A059198 Ratios arising in A005184.
10, 26, 14, 14, 44, 74, 158
Offset: 1
Keywords
Examples
a(1) = 310/31 = 10.
Crossrefs
Cf. A005184.
Extensions
a(7) from Donovan Johnson, Nov 28 2013
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1) = 310/31 = 10.
The Collatz trajectory of 31 begins 31 -> 94 -> 47 -> 142 -> 71 -> 214 -> 107 -> 322 -> 161 -> 484 -> 242 -> 121 -> 364 -> 182 -> 91 -> 274 -> 137 -> 412 -> 206 -> 103 -> 310 -> 155 -> 466 -> ... which contains 310 and 155, both of which are multiples of 31, so 31 is in the sequence. Other than its initial value, the trajectory of 62 is the same as that of 31, so it also includes 310, which is a multiple of 62, so 62 is in the sequence. The trajectory of 671 includes 29524 = 671 * 11 * 2^2, so the sequence includes 671, 671*2 = 1342, and 671*4 = 2684.
a:=[]; for k in [2..40000] do t:=k; while t gt 1 do if IsEven(t) then t:=t div 2; else t:=3*t+1; end if; if IsDivisibleBy(t,k) then a[#a+1]:=k; break; end if; end while; end for; a; // Jon E. Schoenfield, Apr 30 2018
T:= proc(n) option remember; `if`(n=1, 1,
[n, T(`if`(n::even, n/2, 3*n+1))][])
end:
q:= n-> ormap(x-> x>n and irem(x, n)=0, [T(n)]):
select(q, [$1..40000])[]; # Alois P. Heinz, Aug 04 2025
traj[1]:={1};
traj[n_]:=traj[n]=If[EvenQ[n]&&n>0,{n}~Join~traj[n/2],{n}~Join~traj[3*n+1]];
fQ[n_]:=Select[traj[n],IntegerQ[#/n]&&#/n>1&,1]!={};
Select[Range[20000],fQ[#]&] (* Ivan N. Ianakiev, Apr 30 2018 *)
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