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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).

%I A064464 #13 Mar 23 2020 09:46:18
%S A064464 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,
%T A064464 25,28,25,26,31,32,33,34,35,35,37,38,39,39,40,42,43,44,44,46,47,47,47,
%U A064464 48,50,51,51,54,54,56,56,58,59,60,60,59,63,63,63,66,65,67,69,69,70,69
%N 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).
%C A064464 These binary orders are nearly equal to n.
%C A064464 For several values of n, a(n) = n holds, e.g., for n = 1, 2, 3, 5, 6, 8, 9, 10, 11,12.
%F A064464 a(n) = A029837(A060692(n)) = ceiling(log_2(A060692(n))).
%e A064464 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.
%o A064464 (PARI) {for(n=1,72,d=divrem(3^n,2^n); print1(ceil(log(d[1]+d[2])/log(2)),","))}
%Y A064464 Cf. A029837, A060692, A064630.
%K A064464 nonn
%O A064464 1,2
%A A064464 _Labos Elemer_, Oct 03 2001; revised Mar 10 2002
%E A064464 Edited by _Klaus Brockhaus_, May 24 2003