A325597 a(n) is the least number not 2a(m) + a(m-1) for any m < n.

1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 87

Offset

1,2

Comments

Conjectures: Let d(n) = 3a(n) - 4n; then d(n) is bounded, and d(n) = 0 for infinitely many n.

Links

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

Example

Necessarily, a(1) = 1 and a(2) = 2.  Because of these values, 5 is the least number not in the sequence, so that a(3) = 3 and a(4) = 4.  Consequently, 8 and 11 are disallowed, so a(5) = 6 and a(6) = 7.

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; Do[AppendTo[a, mex[Rest[2 a] + Most[a], Last[a] + 1]], {60}]; a  (* A325597 *)
c = Complement[Range[Last[a]], a]  (* A325598 *)
da = Differences[a] (* A325599 *)
Flatten[Position[da, 1]]  (* A325600 *)
Flatten[Position[da, 2]]  (* A325601 *)
(* Peter J. C. Moses, May 07 2019 *)

Crossrefs

Cf. A325598, A325599, A325417.

Sequence in context: A214857 A362443 A175320 * A001953 A230748 A078607

Adjacent sequences: A325594 A325595 A325596 * A325598 A325599 A325600

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2019

Status

approved