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Twice linear

Provider Source Solutions
Codewars 5672682212c8ecf83e000050 JavaScript

Consider a sequence u where u is defined as follows:

  1. The number u(0) = 1 is the first one in u.
  2. For each x in u, then y = 2 * x + 1 and z = 3 * x + 1 must be in u too.
  3. There are no other numbers in u.

Ex: u = [1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, ...]

1 gives 3 and 4, then 3 gives 7 and 10, 4 gives 9 and 13, then 7 gives 15 and 22 and so on...

Task:

Given parameter n the function dbl_linear (or dblLinear...) returns the element u(n) of the ordered (with <) sequence u (so, there are no duplicates).

Example:

dbl_linear(10) should return 22

Note:

Focus attention on efficiency