A114730 One of a family of fractal sequences that transforms into each other.

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

Offset

1,3

Comments

Let A be the sequence A114729 (1, 1, 1, 2, 3, 2, 2, 1, 1, 1, ...), B be the sequence A114730 (1, 1, 2, 2, 1, 1, 1, 2, 3, 4, ...) and C be the sequence A114731 (1, 2, 1, 1, 1, 2, 3, 3, 2, 2, ...). Let D be the sequence A114732 (1, 2, 3, 1, 1, 2, 3, 4, 5, 6, ...), E be the sequence A114733 (1, 2, 1, 2, 3, 4, 5, 3, 1, 1, ...) and F be the sequence A114734 (1, 1, 2, 3, 4, 2, 1, 2, 3, 4, ...). Then:

- A upper trims to B

- B upper trims to C

- C upper trims to A

- A lower trims to C

- B lower trims to A

- C lower trims to B

- D gives the number of times each element of A occurs

- E gives the number of times each element of B occurs

- F gives the number of times each element of C occurs

- A gives the number of times each element of D occurs

- B gives the number of times each element of E occurs

- C gives the number of times each element of F occurs

- D lower trims to E

- E lower trims to F

- F lower trims to D

- D upper trims to F

- E upper trims to D

- F upper trims to E

Links

Table of n, a(n) for n=1..105.

Example

E(9)=1 and that's the third 1 in sequence E, so B(9)=3.

Mathematica

c[n_] := Flatten[ Table[{Range[3 Floor[(k - 1)/2] + 2],
     Table[{i, i}, {i, Floor[k/2] + k, 1, -1}]}, {k, n}]];
uppertrim[list_] := Fold[DeleteCases[#1, #2, 1, 1] &, list, Range[Max[list]]];
lowertrim[list_] := DeleteCases[list - 1, 0];
numbertimes[list_] := Table[Length@Position[Take[list, k], list[[k]]], {k, Length[list]}];
a[n_] := uppertrim[c[n]];
b[n_] := uppertrim[a[n]];
d[n_] := numbertimes[a[n]];
e[n_] := numbertimes[b[n]];
f[n_] := numbertimes[c[n]];
b[6] (* Birkas Gyorgy, Apr 21 2011 *)

Crossrefs

Cf. A114729, A114731, A114732, A114733, A114733.

Sequence in context: A343558 A297877 A027926 * A031282 A085685 A267632

Adjacent sequences: A114727 A114728 A114729 * A114731 A114732 A114733

Keyword

nonn

Author

Kerry Mitchell, Dec 28 2005

Status

approved