%I #12 Feb 22 2020 20:57:36
%S 2,2,2,1,1,2,1,1,2,2,2,1,1,2,4,2,2,1,1,2,1,3,2,2,1,1,2,1,1,1,1,2,2,1,
%T 1,2,1,3,2,2,1,1,2,2,1,1,1,1,2,1,1,2,1,1,2,2,2,1,1,2,4,2,2,1,1,2,1,3,
%U 2,2,1,1,2,2,1,1,2,2,1,1,2,1,3,2,2,1
%N Difference sequence of A325417.
%C See A325417 for a guide to related sequences. Conjecture: all the differences are in {1,2,3,4}; a count of differences d(n) = a(n)-a(n-1) for n=2..10000 follows: 4755 occurrences of d(n) = 1; 4332 of 2; 744 of 3; and 169 of 4.
%H Clark Kimberling, <a href="/A325444/b325444.txt">Table of n, a(n) for n = 1..10000</a>
%e A325417 is given by A(n) = least number not 2*A(m) or 3*A(m)+1 for any m < n, so that A = (1,3,5,7,8,9,11, ...), with differences (2,2,2,1,1,2,...).
%t a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
%t Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
%t IntegerQ]]] &]], {2000}]; a ; (* A325417 *)
%t c = Complement[Range[Last[a]], a] ; (* A325418 *)
%t Differences[a] (* A325444 *)
%t Differences[c] (* A325445 *)
%t (* _Peter J. C. Moses_, Apr 23 2019 *)
%Y Cf. A325417, A325445.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 03 2019
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