A375782 The 2-adic valuation of the result, starting from n, of Collatz steps x -> (3x+1)/2 while odd.

1, 1, 3, 2, 3, 1, 1, 3, 1, 1, 1, 2, 2, 1, 4, 4, 1, 1, 2, 2, 5, 1, 4, 3, 1, 1, 1, 2, 2, 1, 1, 5, 1, 1, 4, 2, 3, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 1, 1, 2, 2, 4, 1, 2, 3, 1, 1, 1, 2, 2, 1, 3, 6, 1, 1, 3, 2, 3, 1, 1, 3, 1, 1, 1, 2, 2, 1, 2, 4, 1, 1, 2, 2, 7, 1, 3

Offset

1,3

Comments

The number of steps is A007814(n+1) and their result is 2*A085062(n).

a(n) = 1 iff A085062(n) is odd, which is when n+1 is in A338691.

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 1..10000

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

Formula

For n == 0 (mod 2), a(n) = A007814(n).

For k > 0, a(2^k-1) = A007814(3^k-1).

a(n) = 1 + A007814(A085062(n)).

Example

7 -> 11 -> 17 -> 26, so a(7) = A007814(26) = 1.

Prog

(PARI) a(n)= valuation((3/2)^valuation(n+1, 2)*(n+1)-1, 2);

Crossrefs

Cf. A007814, A085062, A338691, A363270.

Sequence in context: A085747 A106693 A107335 * A341850 A341847 A200223

Adjacent sequences: A375778 A375780 A375781 * A375783 A375784 A375785

Keyword

nonn,easy

Author

Ruud H.G. van Tol, Aug 28 2024

Status

approved