A297827 Difference sequence of A297826.

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, 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, 1, 6, 2, 1, 2, 6, 2, 3, 1, 2, 4, 1, 2, 2, 4, 3, 1, 4

Offset

1,2

Comments

Conjectures:

(1) 0 <= a(k) <= 6 for k>=1;

(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.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
tbl = {}; a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + n;
b[n_] := b[n] = mex[tbl = Join[{a[n], a[n - 1], b[n - 1]}, tbl], b[n - 1]];
u = Table[a[n], {n, 0, 300}](* A297826 *)
v = Table[b[n], {n, 0, 300}](* A297997 *)
Differences[u];  (* A297827 *)
Differences[v];  (* A297828 *)
(* Peter J. C. Moses, Jan 03 2017 *)

Crossrefs

Cf. A297826, A297828.

Sequence in context: A363252 A070962 A093008 * A198496 A318332 A177925

Adjacent sequences: A297824 A297825 A297826 * A297828 A297829 A297830

Keyword

nonn,easy

Author

Clark Kimberling, Feb 04 2018

Status

approved