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A138103 Numbers with an odd number of 1's in base 6 expansion.

%I A138103 #7 Feb 13 2017 00:18:22
%S A138103 1,6,8,9,10,11,13,19,25,31,36,38,39,40,41,43,48,50,51,52,53,54,56,57,
%T A138103 58,59,60,62,63,64,65,66,68,69,70,71,73,78,80,81,82,83,85,91,97,103,
%U A138103 109,114,116,117,118,119,121,127,133,139,145,150,152,153,154,155,157,163
%N A138103 Numbers with an odd number of 1's in base 6 expansion.
%C A138103 This is to A007092 (numbers in base 6) as A000069 (odious numbers: odd number of 1's in binary expansion) is to A007088 (numbers written in base 2) and as A137469 is to A007091 (numbers in base 5). Note that odd number of 1's in base 3 expansion is simply the odd numbers. This sequence includes, as a subset, A043373 = numbers n such that number of 1's in base 6 is 1.
%C A138103 This is strictly different from A043373.
%C A138103 Terms in this sequence but not in A043374 are 43, 223, 253, 258, 260, 261, 262, 263, 265, 271, 277, 283, 295, ... - _R. J. Mathar_, May 13 2008
%H A138103 <a href="/index/Ar#6-automatic">Index entries for 6-automatic sequences</a>.
%e A138103 a(1) = 1 because 1 base 10 = 1 base 6, which has an odd number (1) of ones.
%e A138103 a(2) = 6 because 6 base 10 = 10 base 6, which has an odd number (1) of ones.
%e A138103 a(3) = 8 because 8 base 10 = 12 base 6, which has an odd number (1) of ones.
%e A138103 a(11) = 36 because 36 base 10 = 100 base 6, which has an odd number (1) of ones.
%e A138103 a(17) = 43 because 43 base 10 = 111 base 6, which has an odd number (3) of ones.
%p A138103 isA138103 := proc(n) local a; a := 0 ; for d in convert(n,base,6) do if d = 1 then a := a+1 ; fi ; od: RETURN( a mod 2 = 1) ; end: for n from 1 to 300 do if isA138103(n) then printf("%d,",n) ; fi ; od: # _R. J. Mathar_, May 13 2008
%Y A138103 Cf. A000069, A007088, A007092, A043373, A137469.
%K A138103 base,easy,nonn,less
%O A138103 1,2
%A A138103 _Jonathan Vos Post_, May 03 2008
%E A138103 Corrected and extended by _R. J. Mathar_, May 13 2008