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A206805 Position of 2^n when {2^j} and {3^k} are jointly ranked; complement of A206807.

%I A206805 #31 Jan 27 2020 07:05:44
%S A206805 1,3,4,6,8,9,11,13,14,16,17,19,21,22,24,26,27,29,30,32,34,35,37,39,40,
%T A206805 42,44,45,47,48,50,52,53,55,57,58,60,61,63,65,66,68,70,71,73,75,76,78,
%U A206805 79,81,83,84,86,88,89,91,92,94,96,97,99,101,102,104,106,107
%N A206805 Position of 2^n when {2^j} and {3^k} are jointly ranked; complement of A206807.
%C A206805 The joint ranking is for j >= 1 and k >= 1, so that the sets {2^j} and {3^k} are disjoint. Not identical to A182774; e.g., A206805 contains 318 but A182774 does not.
%H A206805 Jinyuan Wang, <a href="/A206805/b206805.txt">Table of n, a(n) for n = 1..1000</a>
%F A206805 a(n) = n + floor(n*log_2(3)) (while A206807(n) = n + floor(n*log_3(2))).
%e A206805 The joint ranking begins with 2,3,4,8,9,16,27,32,64,81,128,243,256, so that
%e A206805 this sequence = (1,3,4,6,8,9,11,13,...),
%e A206805 A206807       = (2,5,7,10,12,...).
%t A206805 f[n_] := 2^n; g[n_] := 3^n; z = 200;
%t A206805 c = Table[f[n], {n, 1, z}]; s = Table[g[n], {n, 1, z}];
%t A206805 j = Sort[Union[c, s]];
%t A206805 p[n_] := Position[j, f[n]]; q[n_] := Position[j, g[n]];
%t A206805 Flatten[Table[p[n], {n, 1, z}]] (* A206805 *)
%t A206805 Table[n + Floor[n*Log[3, 2]], {n, 1, 50}] (* A206805 *)
%t A206805 Flatten[Table[q[n], {n, 1, z}]]  (* A206807 *)
%t A206805 Table[n + Floor[n*Log[2, 3]], {n, 1, 50}] (* A206807 *)
%o A206805 (PARI) a(n) = n + floor(n*log(2)/log(3)); \\ _Jinyuan Wang_, Jan 27 2020
%Y A206805 Cf. A182773, A182774, A206807.
%K A206805 nonn
%O A206805 1,2
%A A206805 _Clark Kimberling_, Feb 16 2012