A064464 Binary order (cf. A029837) of the number of parts if 3^n is partitioned into parts of size 2^n as far as possible and into parts of size 1^n (cf. A060692).

1, 2, 3, 3, 5, 6, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 18, 19, 19, 21, 22, 23, 21, 23, 26, 25, 28, 25, 26, 31, 32, 33, 34, 35, 35, 37, 38, 39, 39, 40, 42, 43, 44, 44, 46, 47, 47, 47, 48, 50, 51, 51, 54, 54, 56, 56, 58, 59, 60, 60, 59, 63, 63, 63, 66, 65, 67, 69, 69, 70, 69

Offset: 1

Author

Labos Elemer, Oct 03 2001; revised Mar 10 2002

Keywords

• nonn

Comments

These binary orders are nearly equal to n.

For several values of n, a(n) = n holds, e.g., for n = 1, 2, 3, 5, 6, 8, 9, 10, 11,12.

Examples

			For n=12, 3^12 = 531441 = 129*2^12 + 3057*1^12; the binary order of 129 + 3057 = 3186 is ceiling(log_2(3186)) = 12, the exponent.
		

Crossrefs

Cf. A029837, A060692, A064630.

Programs

PARI

{for(n=1,72,d=divrem(3^n,2^n); print1(ceil(log(d[1]+d[2])/log(2)),","))}

Formula

a(n) = A029837(A060692(n)) = ceiling(log_2(A060692(n))).

Extensions

Edited by Klaus Brockhaus, May 24 2003