A055247 Related to A055246 and A005836. Used for boundaries of open intervals which have to be erased in the Cantor middle third set construction.

1, 2, 7, 8, 19, 20, 25, 26, 55, 56, 61, 62, 73, 74, 79, 80, 163, 164, 169, 170, 181, 182, 187, 188, 217, 218, 223, 224, 235, 236, 241, 242, 487, 488, 493, 494, 505, 506, 511, 512, 541, 542, 547, 548, 559, 560, 565, 566, 649, 650, 655, 656

Offset

1,2

Comments

At step number k >= 1 the 2^(k-1) open intervals which are erased from [0,1] in the Cantor middle third set construction are: I(k,n)=(a(2*n-1)/3^k,a(2*n)/3^k), n=1,.,2^(k-1).

Links

Table of n, a(n) for n=1..52.

Formula

a(n)= A055246((n+1)/2) if n odd, a(n)= A055246(n/2)+1 if n even. A055246(n)= 1+6*A005836(n-1), n >= 1.

a(1) = 1, a(n) = 3^ceiling( log_2( n ) ) - a( 2^ceiling( log_2( n ) ) + 1 - n ). - Juan Jose Alba Gonzalez (jjalba(AT)gmail.com), May 16 2006

Example

k=1: (1/3, 2/3); k=2: (1/9, 2/9), (7/9, 8/9); k=3: (1/27, 2/27), (7/27, 8/27), (19/27, 20/27), (25/27, 26/27); ...

Crossrefs

Cf. A005836, A055246.

Sequence in context: A213037 A287343 A101518 * A015617 A306903 A026579

Adjacent sequences: A055244 A055245 A055246 * A055248 A055249 A055250

Keyword

nonn,easy

Author

Wolfdieter Lang, May 23 2000

Status

approved