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%I #42 Dec 31 2021 06:07:54
%S 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,25,26,27,28,29,
%T 31,32,33,34,35,37,38,39,40,41,43,44,45,46,47,49,50,51,52,53,55,56,57,
%U 58,59,61,62,63,64,65,67,68,69,70,71,73,74,75,76,77,79,80,81,82,83,85,86
%N Numbers that are congruent to {1, 2, 3, 4, 5} mod 6.
%C Numbers that are not divisible by 6. - _Benoit Cloitre_, Jul 11 2009
%C More generally the sequence a(n,m) of numbers not divisible by some fixed integer m >= 2 is given by a(n,m) = n - 1 + floor((n+m-2)/(m-1)). - _Benoit Cloitre_, Jul 11 2009
%H Ivan Panchenko, <a href="/A047253/b047253.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F a(n) = 5 + a(n-5).
%F G.f.: x*(1+x)*(1+x+x^2)*(x^2-x+1) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ).
%F a(n) = n - 1 + floor((n+4)/5). - _Benoit Cloitre_, Jul 11 2009
%F A122841(a(n)) = 0. - _Reinhard Zumkeller_, Nov 10 2013
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (15-4*sqrt(3))*Pi/36. - _Amiram Eldar_, Dec 31 2021
%t Select[Table[n,{n,200}],Mod[#,6]!=0&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2011*)
%o (PARI) a(n)= 1+n+n\5
%o (PARI) a(n)=n-1+floor((n+4)/5) \\ _Benoit Cloitre_, Jul 11 2009
%o (Haskell)
%o a047253 n = n + n `div` 5
%o a047253_list = [1..5] ++ map (+ 6) a047253_list
%o -- _Reinhard Zumkeller_, Nov 10 2013
%Y Cf. A097325, A122841.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E Extended by _R. J. Mathar_, Oct 18 2008
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