A380244 The Collatz (or 3x+1) trajectory starting at a(n) contains exactly n odd integers and a(n) is the n-th number with this property.

1, 10, 12, 68, 45, 30, 72, 101, 134, 179, 237, 314, 422, 551, 723, 509, 1282, 887, 1170, 1535, 2021, 1509, 1899, 2412, 1780, 2217, 3170, 3867, 2819, 3728, 2511, 3155, 3972, 2802, 3578, 2623, 3444, 4302, 3087, 3968, 2690, 1806, 2336, 1593, 2084, 2757, 1884, 2477

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..235

Wikipedia, Collatz Conjecture

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

Formula

A078719(a(n)) = n.

Example

a(2) = 10 is the second integer (after 5) having exactly two odd integers in the Collatz trajectory: 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1.

Maple

b:= proc(n) option remember; irem(n, 2, 'r')+
      `if`(n=1, 0, b(`if`(n::odd, 3*n+1, r)))
    end:
A:= proc() local h, p, q; p, q:= proc() [] end, 0;
      proc(n, k)
        if k=1 then return 2^(n-1) fi;
        while nops(p(k))<n do q:= q+1;
          h:= b(q);
          p(h):= [p(h)[], q]
        od; p(k)[n]
      end
    end():
a:= n-> A(n$2):
seq(a(n), n=1..48);

Crossrefs

Main diagonal of A354236.

Cf. A006577, A006667, A078719, A337144.

Sequence in context: A257039 A337076 A223150 * A333258 A370976 A241252

Adjacent sequences: A380241 A380242 A380243 * A380245 A380246 A380247

Keyword

nonn

Author

Alois P. Heinz, Jan 17 2025

Status

approved