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

1,1

Comments

See A325417 for a guide to related sequences.

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

Links

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

Formula

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

Example

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,...).

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 *)

Crossrefs

Cf. A325417, A036668, A325499.

Sequence in context: A136148 A178252 A338199 * A224850 A269976 A132409

Adjacent sequences: A325495 A325496 A325497 * A325499 A325500 A325501

Keyword

nonn,easy

Author

Clark Kimberling, May 05 2019

Status

approved