A325498 Difference sequence of A036668.

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

Offset: 1

Author

Clark Kimberling, May 05 2019

Keywords

• nonn
• easy

Comments

See A325417 for a guide to related sequences.

Conjecture: every term is in {1,2,3,4}.

Examples

			A036668 is given by A(n) = least number not 2*A(m) or 3*A(m) for any m < n, so that A = (1,4,5,6,7,9,11,...), with differences (3,1,1,1,2,2,...).
		

Links

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

Crossrefs

Cf. A325417, A036668, A325499.

Programs

Mathematica

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/2}],
IntegerQ]]] &]], {2000}]; a ;       (* A036668 *)
c = Complement[Range[Last[a]], a] ; (* A325424 *)
Differences[a]  (* A325498 *)
Differences[c]  (* A325499 *)
(* Peter J. C. Moses, Apr 23 2019 *)

Formula

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = 12/7. - Amiram Eldar, Nov 26 2020