I double checked, and made a few more conjectures on case splitting: 1. Periodic cases: a(c1*(n+1)+c2)=a(c1*n+c2)+c3(c2) {190, 41, 9, 107, 25} -> {A334501, A334509, A334511, A33514, A33513} 2. For large n, a(n)=3 {62, 131} -> {A334502, A334503} 3. Sequence should be viewed as table with rows a(2^n),a(2^n+1),...,a(2^(n+1)-1) {26, 169, 161, 45, 105} -> {A334504, A334505, A334506, A334508, A334512} Also, 73->A334510, but the pattern is not as easy to see. The most interesting case was anomalous 122 -> A334507. It is halfway periodic, only on the even terms: In[]= a[122, 2 #] & /@ Range[1, 20] In[]=a[122, 2 # + 1] & /@ Range[1, 20] Out[]= {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} Out[]= {1, 2, 1, 6, 4, 14, 1, 14, 12, 62, 8, 126, 28, 30, 1, 30, 28, 1022, 24, 126} Highly likely that the second sequence is http://oeis.org/A268754. Comparing with APG's mma def. Jan. 13 2009, definition via C.A. seems the more simple. This looks interesting, but I don't know the convention of A268754, so could not check rigorously just yet. Maybe it is easy though. Adam, is there an isomorphism here? --Brad On Tue, May 5, 2020 at 3:56 PM Neil Sloane <njasloane@gmail.com> wrote:
Brad, Thanks for answering (on April 26) my questions about the period length of rule 30, etc.
I've just created sequences A334496, A334497, and A334501-A334515 as a result of your reply.