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A297827 Difference sequence of A297826.

%I A297827 #4 Feb 04 2018 17:28:23
%S A297827 1,5,2,2,4,3,3,1,2,4,1,4,1,6,2,1,2,6,0,2,6,0,2,2,2,4,5,2,1,2,2,2,4,3,
%T A297827 1,2,2,2,4,3,3,3,1,2,4,1,2,2,4,5,2,3,3,1,2,4,1,6,2,3,3,1,2,4,1,4,1,4,
%U A297827 1,6,2,1,2,6,2,3,1,2,4,1,2,2,4,3,1,4
%N A297827 Difference sequence of A297826.
%C A297827 Conjectures:
%C A297827 (1) 0 <= a(k) <= 6 for k>=1;
%C A297827 (2) if d is in {0,1,2,3,4,5,6}, then a(k) = d for infinitely many k; for d = 0, see A297829.
%H A297827 Clark Kimberling, <a href="/A297827/b297827.txt">Table of n, a(n) for n = 1..10000</a>
%t A297827 mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
%t A297827 tbl = {}; a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
%t A297827 a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + n;
%t A297827 b[n_] := b[n] = mex[tbl = Join[{a[n], a[n - 1], b[n - 1]}, tbl], b[n - 1]];
%t A297827 u = Table[a[n], {n, 0, 300}](* A297826 *)
%t A297827 v = Table[b[n], {n, 0, 300}](* A297997 *)
%t A297827 Differences[u];  (* A297827 *)
%t A297827 Differences[v];  (* A297828 *)
%t A297827 (* _Peter J. C. Moses_, Jan 03 2017 *)
%Y A297827 Cf. A297826, A297828.
%K A297827 nonn,easy
%O A297827 1,2
%A A297827 _Clark Kimberling_, Feb 04 2018