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A047595 Numbers that are congruent to {0, 1, 2, 3, 4, 5, 7} mod 8.

%I A047595 #28 Sep 08 2022 08:44:57
%S A047595 0,1,2,3,4,5,7,8,9,10,11,12,13,15,16,17,18,19,20,21,23,24,25,26,27,28,
%T A047595 29,31,32,33,34,35,36,37,39,40,41,42,43,44,45,47,48,49,50,51,52,53,55,
%U A047595 56,57,58,59,60,61,63,64,65,66,67,68,69,71,72,73,74,75
%N A047595 Numbers that are congruent to {0, 1, 2, 3, 4, 5, 7} mod 8.
%C A047595 Complement of A017137. - _Michel Marcus_, Sep 15 2015
%H A047595 <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 A047595 From _Wesley Ivan Hurt_, Sep 15 2015: (Start)
%F A047595 G.f.: x*(1+x+x^2+x^3+x^4+2*x^5+x^6)/((x-1)^2*(1+x+x^2+x^3+x^4+x^5+x^6)).
%F A047595 a(n) = a(n-1) + a(n-7) - a(n-8) for n>8.
%F A047595 a(n) = n - 1 + floor(n/7). (End)
%F A047595 From _Wesley Ivan Hurt_, Jul 21 2016: (Start)
%F A047595 a(n) = a(n-7) + 8 for n>7.
%F A047595 a(n) = (56*n - 70 - 6*(n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.
%F A047595 a(7*k) = 8*k-1, a(7*k-1) = 8*k-3, a(7*k-2) = 8*k-4, a(7*k-3) = 8*k-5, a(7*k-4) = 8*k-6, a(7*k-5) = 8*k-7, a(7*k-6) = 8*k-8. (End)
%p A047595 A047595:=n->n-1+floor(n/7): seq(A047595(n), n=1..100); # _Wesley Ivan Hurt_, Sep 15 2015
%t A047595 Table[n - 1 + Floor[n/7], {n, 100}] (* _Wesley Ivan Hurt_, Sep 15 2015 *)
%t A047595 LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 7, 8}, 70] (* _Vincenzo Librandi_, Sep 16 2015 *)
%o A047595 (Magma) [n-1+Floor(n/7) : n in [1..100]]; // _Wesley Ivan Hurt_, Sep 15 2015
%o A047595 (Magma) I:=[0,1,2,3,4,5,7,8]; [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..70]]; // _Vincenzo Librandi_, Sep 16 2015
%o A047595 (PARI) vector(200, n, n-1+floor(n/7)) \\ _Altug Alkan_, Oct 23 2015
%Y A047595 Cf. A017137 (8n+6).
%K A047595 nonn,easy
%O A047595 1,3
%A A047595 _N. J. A. Sloane_