OFFSET

0,3

COMMENTS

In other words, the n-th row contains the numbers k with the same binary length as n and for any i >= 0, if the i-th bit and the (i+1)-th bit in k are different then they are also different in n (i = 0 corresponding to the least significant bit).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..9841 (rows for n = 0..511 flattened)

EXAMPLE

Triangle begins (in decimal and in binary):

n n-th row bin(n) n-th row in binary

-- ------------ ------ ------------------

0 0 0 0

1 1 1 1

2 2, 3 10 10, 11

3 3 11 11

4 4, 7 100 100, 111

5 4, 5, 6, 7 101 100, 101, 110, 111

6 6, 7 110 110, 111

7 7 111 111

8 8, 15 1000 1000, 1111

9 8, 9, 14, 15 1001 1000, 1001, 1110, 1111

.

For n = 9:

- the binary expansion of 9 is "1001",

- the corresponding run lengths are 1, 2, 1,

- so the 9th row contains the values with the following run lengths:

1, 2, 1 -> 9 ("1001" in binary)

1, 2+1 -> 8 ("1000" in binary)

1+2, 1 -> 14 ("1110" in binary)

1+2+1 -> 15 ("1111" in binary)

PROG

(PARI) row(n) = { my (r = []); while (n, my (v = valuation(n+n%2, 2)); n \= 2^v; r = concat(v, r)); my (s = [if (#r, 2^r[1]-1, 0)]); for (k = 2, #r, s = concat(s * 2^r[k], [(h+1)*2^r[k]-1|h<-s]); ); vecsort(s); }

CROSSREFS

KEYWORD

nonn,base,tabf

AUTHOR

Rémy Sigrist, Mar 19 2023

STATUS

approved