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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
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
1,2
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.
FORMULA
a(n) = A029837(A060692(n)) = ceiling(log_2(A060692(n))).
EXAMPLE
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.
PROG
(PARI) {for(n=1, 72, d=divrem(3^n, 2^n); print1(ceil(log(d[1]+d[2])/log(2)), ", "))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 03 2001; revised Mar 10 2002
EXTENSIONS
Edited by Klaus Brockhaus, May 24 2003
STATUS
approved