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A297828 Difference sequence of A297997.

%I A297828 #4 Feb 06 2018 19:27:04
%S A297828 1,1,1,2,2,2,1,1,2,1,2,1,3,2,1,1,3,1,1,3,1,1,1,1,2,3,2,1,1,1,1,2,2,1,
%T A297828 1,1,1,2,2,2,2,1,1,2,1,1,1,2,3,2,2,2,1,1,2,1,3,2,2,2,1,1,2,1,2,1,2,1,
%U A297828 3,2,1,1,3,2,2,1,1,2,1,1,1,2,2,1,2,1
%N A297828 Difference sequence of A297997.
%C A297828 Conjectures:
%C A297828 (1) 2 <= a(k) <= 4 for k>=1;
%C A297828 (2) if d is in {1,2,3}, then a(k) = d for infinitely many k.
%H A297828 Clark Kimberling, <a href="/A297828/b297828.txt">Table of n, a(n) for n = 1..10000</a>
%t A297828 mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
%t A297828 tbl = {}; a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
%t A297828 a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + n;
%t A297828 b[n_] := b[n] = mex[tbl = Join[{a[n], a[n - 1], b[n - 1]}, tbl], b[n - 1]];
%t A297828 u = Table[a[n], {n, 0, 300}](* A297826 *)
%t A297828 v = Table[b[n], {n, 0, 300}](* A297997 *)
%t A297828 Differences[u];  (* A297827 *)
%t A297828 Differences[v];  (* A297828 *)
%t A297828 (* _Peter J. C. Moses_, Jan 03 2017 *)
%Y A297828 Cf. A297826, A297827.
%K A297828 nonn,easy
%O A297828 1,4
%A A297828 _Clark Kimberling_, Feb 04 2018