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

Author

Wolfdieter Lang, May 23 2000

Keywords

• nonn
• easy

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).

Examples

			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.

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