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%I #36 Oct 20 2019 06:05:12
%S 3,2,1,6,3,2
%N When a prime-based mapping reaches 0.
%C 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.
%C 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.
%C Conjecture: a(n) > 0 for all n.
%C 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.
%H Nicholas Matteo, <a href="/A323417/a323417_1.txt">Known values for n in 0 .. 1000</a>
%Y A309222 is the trajectory of this mapping with n_0 = 6.
%K nonn,more
%O 0,1
%A _Hugo van der Sanden_, Aug 30 2019
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