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Positive numbers that are not multiples of 12.
4

%I #13 Jan 16 2020 20:20:21

%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,

%T 29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,

%U 54,55,56,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78

%N Positive numbers that are not multiples of 12.

%C A168185(a(n)) = 1; complement of A008594;

%C A109015(a(n)) < 12.

%C 121 (in decimal) is a member of this sequence but not a member of A023805. - _Robert Munafo_, Jan 26 2010

%C 80 is a member of this sequence but is not a member of A160453. - _Franklin T. Adams-Watters_, Jan 26 2010

%H G. C. Greubel, <a href="/A168186/b168186.txt">Table of n, a(n) for n = 1..1000</a>

%F From _Chai Wah Wu_, Jan 16 2020: (Start)

%F a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.

%F G.f.: x*(x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/(x^12 - x^11 - x + 1). (End)

%e 156 is in A023805 but not in this sequence. - _Franklin T. Adams-Watters_, Jan 26 2010

%t Select[Table[n,{n,200}],Mod[#,12]!=0&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2011*)

%Y All three of A023805, A160453, A168186 are different.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Nov 30 2009