A325524 Difference sequence of A325431.

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

Offset: 1

Author

Clark Kimberling, May 06 2019

Keywords

• nonn
• easy

Comments

See A325417 for a guide to related sequences.

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

Links

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

Crossrefs

Cf. A325417, A325431, A325525.

Programs

Mathematica

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/4}],
IntegerQ]]] &]], {20000}]; a;         (* A315431 *)
c = Complement[Range[Last[a]], a] ;   (* A325432 *)
Differences[a]  (* A325524 *)
Differences[c]  (* A325525 *)
(* Peter J. C. Moses, Apr 23 2019 *)

Formula

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = 20/13. - Amiram Eldar, Nov 26 2020