A337144 n is the a(n)-th positive integer which takes its number of steps to reach 1 in the Collatz (or 3x+1) problem.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 1, 3, 1, 2, 3, 4, 1, 1, 1, 2, 3, 2, 3, 1, 2, 2, 1, 3, 2, 4, 5, 1, 2, 2, 1, 2, 3, 2, 3, 4, 1, 1, 1, 2, 5, 3, 4, 1, 2, 3, 5, 1, 2, 4, 5, 1, 2

Offset: 1

Author

Alois P. Heinz, Jan 27 2021

Keywords

• nonn
• look

Examples

			a(13) = 2 because A006577(13) = A006577(12) = 9 != A006577(j) for j < 12.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..65536
• Wikipedia, Collatz Conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A005186, A006577, A380244.

Programs

Maple

collatz:= proc(n) option remember; `if`(n=1, 0,
   1 + collatz(`if`(n::even, n/2, 3*n+1)))
end:
b:= proc() 0 end:
a:= proc(n) option remember; local t;
     `if`(n=1, 0, a(n-1));
      t:= collatz(n); b(t):= b(t)+1
    end:
seq(a(n), n=1..120);

Mathematica

collatz[n_] := collatz[n] = If[n == 1, 0,
   1 + collatz[If[EvenQ[n], n/2, 3n+1]]];
b[_] = 0;
a[n_] := a[n] = Module[{t},
   If[n == 1, 0, a[n-1]];
   t = collatz[n]; b[t] = b[t]+1];
Array[a, 120] (* Jean-François Alcover, Jan 29 2021, after Alois P. Heinz *)

Formula

Ordinal transform of A006577.

a(n) = |{ j in {1..n} : A006577(j) = A006577(n) }|.