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

Author

Alois P. Heinz, Jan 17 2025

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

Main diagonal of A354236.

Cf. A006577, A006667, A078719, A337144.

Programs

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)) A(n$2):
seq(a(n), n=1..48);

Formula

A078719(a(n)) = n.