A323417 When a prime-based mapping reaches 0.

3, 2, 1, 6, 3, 2

Offset: 0

Author

Hugo van der Sanden, Aug 30 2019

Keywords

• nonn
• more

Comments

Writing p_i for the i-th prime, A000040(i); let n_0 = n, and apply the mapping n_i = n_{i-1} + p_i (if p_i > n_{i-1}) else n_{i-1} - p_i. Then a(n) is the least k > 0 for which n_k = 0, or -1 if no such k exists.

In the traversal of n_i for a given n, if it reaches a local minimum after subtracting p_i, it will next reach a local minimum at p_j which will be close to 3p_i.

Conjecture: a(n) > 0 for all n.

For n in { 6 16 20 30 42 50 51 56 70 76 84 85 90 92 }, a(n) is unknown; in each case either a(n) = -1 or a(n) > 2 * 10^12. a(n) is known for all other n <= 100: see the A-file for details.

Links

• Nicholas Matteo, Known values for n in 0 .. 1000

Crossrefs

A309222 is the trajectory of this mapping with n_0 = 6.