Definitions
Collatz sequence: p_i ∈ N⁺ ∧ p_i is odd, for i > 0: p_i = (3p_{i - 1} + 1) / d_{i - 1}. The Collatz divisor d_{i - 1} = 2^{x_{i - 1}}, in which x_{i - 1} is the number of times that (3p _{i - 1} + 1) is divided by 2 to reach the odd p_i. Notation: p₀ (d₀) p₁ (d₁) p₂ (d₂) ... p_{n - 1} (d_{n - 1}) p_n | p_n = 1.
Length: For all positive odd integers p: n is the Length of p if n is the lowest index i for which p_i = 1. Notation: Lth(p) = n.
Evenness: For all positive odds p > 1, s is called the Evenness of p if s is the sum of the exponents x_i for 0 ≤ i ≤ (n - 1) of the Collatz divisors d_i = 2^x_i.
Notation: Evn(p) = s.
Rho: 2^Evn(p) / (p • 3^Lth(p)). Notation: Rho(p).

Appropriate other programs on this site
For the above (and other) computational properties of Collatz sequences, see: Computational properties of Collatz sequences.
For the Collatz equation (below) of any odd integer p, see: Collatz equation.
For a comparable program, for all variables of the Collatz equation, see Variables of the equation of reduced Collatz sequences and Comment.
See also the program Equal Length of reduced Collatz sequences of neighboring positive odds.
For a listing of all possibilities (combinatorial compositions) for calculated p-values (fitting or not), see: Constrained combinatorial compositions and Collatz sequences and Comment
See also the program Constrained compositions of Collatz divisor exponents and Comment. This program finds reduced Collatz sequences of odds p having n = Lth(p) ∧ s = Evn(p) and their compositions by screening adjustable batches of maximal 3000 positive odds. The odds are allowed to have up to 12 digits. Maximum sequence Length: 250; maximum sequence Evenness: 550.

Collatz equation
p₀.3ⁿ + [3^{n - 1} + 3^{n - 2}.2^x₀ + 3^{n - 3}.2^{x₀ + x₁} + 3^{n - 4}.2^{x₀ + x₁ + x₂} + ... + 3.2^{x₀ + x₁ + x₂ + ... + x_{n - 3}} + 2^{x₀ + x₁ + x₂ + ... + x_{n - 2}}] = 2^{x₀ + x₁ + x₂ + ... + x_{n - 1}}

Program variables and sequence fitting
A = 2^s - p.3ⁿ = 2^{x₀ + x₁ + x₂ + ... + x_{n - 1}} - p.3ⁿ = 3^{n - 1} + 3^{n - 2}.2^x₀ + 3^{n - 3}.2^{x₀ + x₁} + 3^{n - 4}.2^{x₀ + x₁ + x₂} + ... + 3.2^{x₀ + x₁ + x₂ + ... + x_{n - 3}} + 2^{x₀ + x₁ + x₂ + ... + x_{n - 2}}
n = Lth(p) = the number of iterations to reach 1.
s = Evn(p) = the sum of the exponents x_i of the Collatz divisors d_i.
n_max = 25 in our program and 25 ≤ s_max ≤ 39. s_max is made dependent on n: to keep calculation time reasonably.
The program calculates the minimum and maximum value of A:
Any Collatz divisor is at least 2 (x_i ≥ 1) and for p > 1 the final Collatz divisor is at least 16 (x_{n - 1} ≥ 4). From these A-values the corresponding p-values are calculated (not necessarily positive and integer). The minimum p-value is rounded to the nearest higher positive odd integer, the maximum p-value is rounded to the nearest lower positive odd integer p. The program investigates the odd integers from p_min to p_max for Lth(p) = n and Evn(p) = s.