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%I #46 Sep 08 2022 08:44:57
%S 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,25,26,27,28,
%T 29,30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,
%U 55,57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,81
%N Numbers that are congruent to {1, 2, 3, 4, 5, 6, 7} mod 8.
%C Or, numbers that are not multiples of 8. - _Benoit Cloitre_, Jul 11 2009
%C More generally the sequence 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
%C Complement of A008590. - _Reinhard Zumkeller_, Nov 30 2009
%H Vincenzo Librandi, <a href="/A047592/b047592.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F a(n) = n - 1 + floor((n+6)/7). - _Benoit Cloitre_, Jul 11 2009
%F A168181(a(n)) = 1. - _Reinhard Zumkeller_, Nov 30 2009
%F From _R. J. Mathar_, Mar 08 2011: (Start)
%F a(n) = a(n-1) + a(n-7) - a(n-8) for n>8.
%F G.f.: x*(1+x)*(1+x^2)*(1+x^4) / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ). (End)
%F a(n) = A207481(n) for n <= 70. - _Reinhard Zumkeller_, Feb 18 2012
%F From _Wesley Ivan Hurt_, Jul 20 2016: (Start)
%F a(n) = (56*n - 28 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) - 6*((n+6) mod 7))/49.
%F a(7k) = 8k-1, a(7k-1) = 8k-2, a(7k-2) = 8k-3, a(7k-3) = 8k-4, a(7k-4) = 8k-5, a(7k-5) = 8k-6, a(7k-6) = 8k-7. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (4*sqrt(sqrt(2)+2) - 2*sqrt(2) - 1)*Pi/16. - _Amiram Eldar_, Dec 28 2021
%p A047592:=n->8*floor(n/7)+[1, 2, 3, 4, 5, 6, 7][(n mod 7)+1]: seq(A047592(n), n=0..100); # _Wesley Ivan Hurt_, Jul 20 2016
%t Complement[Range[88], 8Range[11]] (* _Harvey P. Dale_, Jan 22 2011 *)
%t CoefficientList[Series[(1 + x)*(1 + x^2)*(1 + x^4)/((x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x - 1)^2), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jan 06 2013 *)
%o (PARI) a(n)=n-1+floor((n+6)/7) \\ _Benoit Cloitre_, Jul 11 2009
%o (Magma) [ n: n in [0..100] | n mod 8 in {1, 2, 3, 4, 5, 6, 7} ]; // _Vincenzo Librandi_, Dec 25 2010]
%Y Cf. A008590, A168181, A207481.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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