A346965 a(n) is the number of ascending subsequences in reducing n to 1 using the Collatz reduction, or -1 if n refutes the Collatz conjecture.

0, 0, 1, 0, 1, 1, 3, 0, 4, 1, 3, 1, 2, 3, 2, 0, 3, 4, 4, 1, 1, 3, 2, 1, 5, 2, 17, 3, 4, 2, 16, 0, 6, 3, 2, 4, 4, 4, 6, 1, 17, 1, 6, 3, 4, 2, 16, 1, 5, 5, 5, 2, 2, 17, 17, 3, 7, 4, 6, 2, 3, 16, 15, 0, 6, 6, 5, 3, 3, 2, 16, 4, 18, 4, 2, 4, 5, 6, 6, 1, 4, 17, 17

Offset

1,7

Comments

In this sequence, a subsequence is considered ascending for as long as a (3*n + 1) / 2 step is required.

Links

Douglas Boffey, Table of n, a(n) for n = 1..20000

Douglas Boffey, Code used for generating b-file

Formula

a(2^n) = 0.

a((2^n*(2*x+1)-1) * 2^y) = a(3^n*(2*x+1)-1) + 1, where x, y >= 0.

Example

a(9) = 4, viz.
  9->14;
  14->7->11->17->26;
  26->13->20;
  20->10->5->8.

Prog

(C) /* A007814 */
int num_clear_bits(unsigned n) {
  if (n == 0)
    return -1;
  return log2(n & -n);
}
int A346965(unsigned n) {
  int x;
  int result = 0;
  n >>= num_clear_bits(n);
  while (n > 1) {
    x = num_clear_bits(n + 1);
    n = ((n >> x) + 1) * pow(3, x) - 1;
    n >>= num_clear_bits(n);
    ++result;
  }
  return result;
}

Crossrefs

Cf. A070168, A078719, A221469.

Sequence in context: A129718 A127375 A238573 * A325491 A306803 A319974

Adjacent sequences: A346962 A346963 A346964 * A346966 A346967 A346968

Keyword

nonn

Author

Douglas Boffey, Aug 09 2021

Status

approved