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%I #7 Jun 17 2013 14:33:40
%S 2,4,5,7,9,10,12,14,15,17,18,20,22,23,25,27,28,30,31,33,35,36,38,40,
%T 41,43,45,46,48,49,51,53,54,56,58,59,61,62,64,66,67,69,71,72,74,76,77,
%U 79,80,82,84,85,87,89,90,92,93,95,97,98,100,102,103,105,107
%N Complement of A122437.
%C Suppose that b and c are integers satisfying 1 < b < c. Let x = 1 + log_b(c) and y = 1 + log_c(b). Jointly rank all the numbers b^k for k>=0 and c^k for k>=1; then for n >= 0, the position of b^n is 1 + floor(n*y), and for n >=1, the position of c^n is 1+ floor(n*x).
%C These position sequences are closely related to the Beatty sequences given by floor(n*x) and floor(n*y).
%H Clark Kimberling, <a href="/A226720/b226720.txt">Table of n, a(n) for n = 1..2000</a>
%e The joint ranking of the powers of 2 and of 3 begins like this: 1, 2, 3, 4, 8, 9, 16, 27, 32, 64. The numbers 2^n for n >= 1 are in positions 2, 4, 5, 7, 9, 10.
%t b = 2; c=3; Floor[1 + Range[0, 100]*(1 + Log[b, c])] (* A123384 *)
%t Floor[1 + Range[1, 100]*(1 + Log[c, b])] (* A226721 *)
%Y Cf. A123384, A226721.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 16 2013
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