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A297828 Difference sequence of A297997. 2

%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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Last modified March 20 07:42 EDT 2019. Contains 321345 sequences. (Running on oeis4.)