A337150 Nonnegative integers in the order in which they appear first in A006577.

0, 1, 7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 17, 4, 12, 20, 15, 10, 23, 111, 18, 106, 26, 13, 21, 34, 109, 29, 104, 11, 24, 112, 32, 107, 27, 102, 22, 115, 35, 110, 30, 92, 105, 118, 25, 87, 38, 100, 113, 69, 33, 95, 46, 108, 121, 28, 41, 90, 103, 116, 36, 85, 54

Offset

1,3

Comments

This is A006577 with duplicates removed.

This is a permutation of the nonnegative integers.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Wikipedia, Collatz Conjecture

Index entries for sequences that are permutations of the nonnegative integers

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

a(n) = A006577(A337149(n)).

a(n) = A006577(n) for 1 <= n <= 12.

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:
g:= proc(n) option remember; local t;
     `if`(n=1, 0, g(n-1));
      t:= collatz(n); b(t):= b(t)+1
    end:
h:= proc(n) option remember; local k; for k
      from 1+h(n-1) while g(k)>1 do od; k
    end: h(0):=0:
a:= n-> collatz(h(n)):
seq(a(n), n=1..100);

Mathematica

collatz[n_] := collatz[n] = If[n==1, 0,
   1 + collatz[If[EvenQ[n], n/2, 3n+1]]];
b[_] = 0;
g[n_] := g[n] = Module[{t}, If[n==1, 0, g[n-1]];
   t = collatz[n]; b[t] = b[t]+1];
h[n_] := h[n] = Module[{k}, For[k = 1+h[n-1],
   g[k]>1, k++]; k]; h[0] = 0;
a[n_] := a[n] = collatz[h[n]];
Array[a, 100] (* Jean-François Alcover, Jan 30 2021, after Alois P. Heinz *)

Crossrefs

Cf. A006577, A337149.

Sequence in context: A340420 A127885 A006577 * A280234 A368383 A073652

Adjacent sequences: A337147 A337148 A337149 * A337151 A337152 A337153

Keyword

nonn,look

Author

Alois P. Heinz, Jan 27 2021

Status

approved