A325498 - OEIS

%I #11 Nov 26 2020 03:18:00

%S 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,

%T 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,

%U 1,2,1,1,3,1,2,4,2,4,1,1,1,3,1,1,3,1

%N Difference sequence of A036668.

%C See A325417 for a guide to related sequences.

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

%H Clark Kimberling, <a href="/A325498/b325498.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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,...).

%t a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,

%t Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/2}],

%t IntegerQ]]] &]], {2000}]; a ;       (* A036668 *)

%t c = Complement[Range[Last[a]], a] ; (* A325424 *)

%t Differences[a]  (* A325498 *)

%t Differences[c]  (* A325499 *)

%t (* _Peter J. C. Moses_, Apr 23 2019 *)

%Y Cf. A325417, A036668, A325499.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, May 05 2019