A163491 A fractal sequence (if we delete the first occurrence of n we get the sequence itself).

1, 1, 1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 5, 2, 4, 6, 3, 1, 7, 5, 2, 8, 4, 6, 9, 3, 1, 10, 7, 5, 11, 2, 8, 12, 4, 6, 13, 9, 3, 14, 1, 10, 15, 7, 5, 16, 11, 2, 17, 8, 12, 18, 4, 6, 19, 13, 9, 20, 3, 14, 21, 1, 10, 22, 15, 7, 23, 5, 16, 24, 11, 2, 25, 17, 8, 26, 12

Offset

1,4

Comments

Write the positive integers with two spaces between each integer: 1,_,_,2,_,_,3,_,_,4,_,_,5,_,_,6,..., and fill undefined places with the sequence itself. A003602 is obtained by starting from 1,_,2,_,3,_,4,_,5,_,6,....

From Peter Munn, Aug 02 2020: (Start)

a(n) - 1 is the row of A083044 in which n occurs.

The m-th occurrence of m is at position A083045(m-1).

(End)

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(3n-2) = n.

A083044(a(n) - 1, A087088(n) - 1) = n. - Peter Munn, Aug 02 2020

From Rémy Sigrist, Jan 15 2021: (Start)

a(n+ceiling(n/2)) = a(n).

a(n) = 1 iff n belongs to A061419.

(End)

a(n) = (n+2)/3 if n == 1 (mod 3), otherwise a(n) = a(floor(n*2/3)). - Michael S. Branicky and Kevin Ryde, Jan 16 2021

Example

  1,_,_,2,_,_,3,_,_,4,... -->
  1,1,_,2,_,_,3,_,_,4,... -->
  1,1,1,2,_,_,3,_,_,4,... -->
  1,1,1,2,1,_,3,_,_,4,... -->
  1,1,1,2,1,2,3,_,_,4,... -->
  1,1,1,2,1,2,3,_,_,4,... -->
  1,1,1,2,1,2,3,1,_,4,... -->
  1,1,1,2,1,2,3,1,2,4,... -->
  ...

Mathematica

a[n_] := a[n] = If[Mod[n, 3] == 1, (n+2)/3, a[Floor[2n/3]]];
Array[a, 100] (* Jean-François Alcover, Jan 10 2022 *)

Prog

(Python)
def a(n): return (n+2)//3 if n%3==1 else a(n*2//3)
print([a(n) for n in range(1, 78)]) # Michael S. Branicky, Jan 16 2021
(PARI) a(n) = n+=2; my(q, r); while([q, r]=divrem(n, 3); r, n-=q); q; \\ Kevin Ryde, Jan 16 2021

Crossrefs

Cf. A003602, A007494, A061419, A083044, A083045.

Ordinal transform of A087088.

Sequence in context: A194917 A194914 A195076 * A080772 A259324 A216274

Adjacent sequences: A163488 A163489 A163490 * A163492 A163493 A163494

Keyword

nonn

Author

Benoit Cloitre, Jul 29 2009

Extensions

Terms after a(70) corrected by Jon E. Schoenfield, Nov 26 2015

Status

approved