0,3

The n-th row differs from the prior row only by the presence of n. See A088371 for the positions in the n-th row that n is inserted.

Comment from Clark Kimberling (ck6(AT)evansville.edu), Aug 02 2007: (Start) At A131966, this sequence is cited as the fractal sequence of the Cantor set C.

Recall that C is the set of fractions in [0,1] whose base 3 representation consists solely of 0s and 2s.

Arrange these fractions as follows:

0

0, .2

0, .02, .2

0, .02, .2, .22

0, .002, .02, .2, .22, etc.

Replace each number x by its order of appearance, counting each distinct predecessor of x only once, getting

1

1 2

1 3 2

1 3 2 4

1 5 3 2 4.

Concatenate these to get the current sequence, which is a fractal sequence as defined in "Fractal sequences and interspersions".

One property of such a sequence is that it properly contains itself as a subsequence (infinitely many times). (End)

Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168.

T(n, n)=2^(floor(log(n)/log(2))). Construction. The 2n-th row is the concatenation of row n, after multiplying each term by 2 and subtracting 1, with row n, after multiplying each term by 2. The (2n-1)-th row is the concatenation of row n, after multiplying each term by 2 and subtracting 1, with row n-1, after multiplying each term by 2.

Row 5 is formed from row 3, {1,3,2}, and row 2, {1,2}: {1,5,3,2,4} = {1*2-1,3*2-1,2*2-1}|{1*2,2*2}.

Rows are: {1}, {1, 2}, {1, 3, 2}, {1, 3, 2, 4}, {1, 5, 3, 2, 4}, {1, 5, 3, 2, 6, 4}, {1, 5, 3, 7, 2, 6, 4}, ...

Cf. A088371.

Sequence in context: A085014 A082074 A132283 this_sequence A113787 A115624 A076291

Adjacent sequences: A088367 A088368 A088369 this_sequence A088371 A088372 A088373

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Sep 28 2003