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

Author

Ruud H.G. van Tol, Aug 28 2024

Keywords

• nonn
• easy

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.

Examples

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

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

Crossrefs

Cf. A007814, A085062, A338691, A363270.

Programs

PARI

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

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)).