A288577 Image of 0 under repeated application of the morphism phi = {x -> x,x+1,x+2 if x mod 3 = 0; x -> x+1 if x mod 3 = 1 or 2, for x = 0,1,2,3,...}.

0, 1, 2, 2, 3, 3, 3, 4, 5, 3, 4, 5, 3, 4, 5, 5, 6, 3, 4, 5, 5, 6, 3, 4, 5, 5, 6, 6, 6, 7, 8, 3, 4, 5, 5, 6, 6, 6, 7, 8, 3, 4, 5, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 7, 8, 8, 9, 3, 4, 5, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 7, 8, 8, 9, 3, 4, 5, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 7, 8, 8, 9, 6, 7, 8, 8, 9, 6, 7, 8, 8, 9, 9, 9, 10, 11

Offset: 0

Author

N. J. A. Sloane, Jul 01 2017

Keywords

• nonn

Comments

An analog of A104324 when "Fibonacci" is replaced with "tribonacci".

From Kerry Mitchell, Jul 01 2017: (Start)

This is the limit of a series of iterations. The length of each iteration is given by A000213, beginning with the second term of that sequence (1, 3, 5, 9, 17, etc.):

0

0, 1, 2

0, 1, 2, 2, 3

0, 1, 2, 2, 3, 3, 3, 4, 5

0, 1, 2, 2, 3, 3, 3, 4, 5, 3, 4, 5, 3, 4, 5, 5, 6

etc.

When written in blocks this way, each subsequent block is the concatenation of the previous block, the third-previous block with each term incremented by 3, and the second-previous block, with each term incremented by 3. (End)

References

• Kerry Mitchell, Posting to Sequence Fans Mailing List, Jun 30 2017

Links

• Kerry Mitchell, Table of n, a(n) for n = 0..13744

Crossrefs

Cf. A104324.

Programs

Mathematica

SubstitutionSystem[{x_ -> If[Mod[x, 3] == 0, {x, x+1, x+2}, {x+1}]}, {0}, 7] // Last (* Jean-François Alcover, Jan 21 2018 *)

Extensions

More terms from Kerry Mitchell, Jul 01 2017