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