A325444 Difference sequence of A325417.

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

Offset

1,1

Comments

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.

Links

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

Example

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,...).

Mathematica

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
IntegerQ]]] &]], {2000}]; a ;       (* A325417 *)
c = Complement[Range[Last[a]], a] ; (* A325418 *)
Differences[a]  (* A325444 *)
Differences[c]  (* A325445 *)
(* Peter J. C. Moses, Apr 23 2019 *)

Crossrefs

Cf. A325417, A325445.

Sequence in context: A195052 A104637 A188795 * A058745 A275333 A108393

Adjacent sequences: A325441 A325442 A325443 * A325445 A325446 A325447

Keyword

nonn,easy

Author

Clark Kimberling, May 03 2019

Status

approved