OFFSET
1,2
EXAMPLE
b = A298296 = (3,4,5,6,7,8,9,10,11,12,14,15,17,...), so that b(k+1) = b(k) + 1 for k = 1..9 and b(11) = b(10) + 2.
MATHEMATICA
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5;
a[n_] := a[0]*b[n] + a[1]*b[n - 1]
Table[{a[n], b[n + 1] = mex[Flatten[Map[{a[#], b[#]} &, Range[0, n]]], b[n - 0]]}, {n, 2, 1000}];
u = Table[b[n], {n, 0, 150}] (* A298296 *)
d = Differences[u]
Flatten[Position[d, 1]] (* A298297 *)
Flatten[Position[d, 2]] (* A298298 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 12 2018
STATUS
approved