A363270 The result, starting from n, of Collatz steps x -> (3x+1)/2 while odd, followed by x -> x/2 while even.

1, 1, 1, 1, 1, 3, 13, 1, 7, 5, 13, 3, 5, 7, 5, 1, 13, 9, 11, 5, 1, 11, 5, 3, 19, 13, 31, 7, 11, 15, 121, 1, 25, 17, 5, 9, 7, 19, 67, 5, 31, 21, 49, 11, 17, 23, 121, 3, 37, 25, 29, 13, 5, 27, 47, 7, 43, 29, 67, 15, 23, 31, 91, 1, 49, 33, 19, 17, 13, 35, 121, 9, 55

Offset

1,6

Comments

Each x -> (3x+1)/2 step decreases the number of trailing 1-bits by 1 so A007814(n+1) of them, and the result of those steps is 2*A085062(n).

Links

Dustin Theriault, Table of n, a(n) for n = 1..10000

Formula

a(n) = OddPart((3/2)^A007814(n+1)*(n+1) - 1), where OddPart(t) = A000265(t).

a(n) = OddPart(A085062(n)).

Mathematica

OddPart[x_] := x / 2^IntegerExponent[x, 2]
Table[OddPart[(3/2)^IntegerExponent[i + 1, 2] * (i + 1) - 1], {i, 100}]

Prog

(C) int a(int n) {
  while (n & 1) n += (n >> 1) + 1;
  while (!(n & 1)) n >>= 1;
  return n;
}
(PARI) oddpart(n) = n >> valuation(n, 2); \\ A000265
a(n) = oddpart((3/2)^valuation(n+1, 2)*(n+1) - 1); \\ Michel Marcus, May 24 2023

Crossrefs

Cf. A000265, A085062.

Cf. A160541 (number of iterations).

Cf. A075677.

Sequence in context: A215240 A068697 A010258 * A107774 A253685 A122478

Adjacent sequences: A363267 A363268 A363269 * A363271 A363272 A363273

Keyword

nonn,easy

Author

Dustin Theriault, May 23 2023

Status

approved