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%I #2 Mar 30 2012 17:39:58
%S 1,2,3,8,4,6,13,18,40,20,121,24,364,26,9,80,10,242,12,728,27,2186,28,
%T 6560,30,19682,31,59048,36,177146,37,531440,39,1594322,81,4782968,82,
%U 14348906,84,43046720,85,129140162,90,387420488,91,1162261466,93
%N a(n) is the smallest integer not yet in the sequence with no common base-3 digit with a(n-1).
%C Numbers of A031944 do not appear in this sequence. After a number which has base-3 digits 0 and 1, a number of the form 3^k-1 (see A024023) follows by definition, because its base-3 digits are all 2.
%e The 4th term cannot be 4 because 4(base10)=11(base3) shares a common digit 1 with a(3)=3(base10)=10(base3). It cannot be 5(base10)=12(base3) because this shares the digit 1 with 3=10(base3). It cannot be 6(base10)=20(base3) because this shares the digit 0 with 3=10(base3). It cannot be 7(base10)=21(base3) because this shares the digit 1 with 3=10(base3). It becomes a(4)=8(base10)=22(base3) which does not have the digit 0 or 1 of a(3)=10(base3).
%Y Cf. A067581 (base-10), A158929 (base-4), A158930 (base-5).
%K base,easy,nonn
%O 1,2
%A _R. J. Mathar_, Mar 31 2009