|
| |
|
|
A163491
|
|
A fractal sequence (if we delete the first occurrence of n we get the sequence itself).
|
|
5
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
