OFFSET
0,1
COMMENTS
The conditions that (a(n)) and (b(n)) be increasing and complementary force the equation a(n) = 5 b(n+1) - b(n), with initial value b(0) = 1, to have a unique solution; that is, a pair of complementary sequences (a(n)) = (9,13,17,21,25,29,...) and (b(n)) = (1,2,3,4,5,6,7,8,10, ...). Conjecture: {a(n) - 5 n} is unbounded below and above.
EXAMPLE
(See A329387.)
MATHEMATICA
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
b = {1}; a = {}; h = 5;
Do[AppendTo[b, mex[Flatten[{a, b}], b[[-1]]]];
AppendTo[a, h b[[-1]] - b[[-2]]], {250}]; a
(* Peter J. C. Moses, Sep 07 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 23 2019
STATUS
approved