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

%I #32 Sep 08 2022 08:44:57

%S 0,1,2,3,4,5,8,9,10,11,12,13,16,17,18,19,20,21,24,25,26,27,28,29,32,

%T 33,34,35,36,37,40,41,42,43,44,45,48,49,50,51,52,53,56,57,58,59,60,61,

%U 64,65,66,67,68,69,72,73,74,75,76,77,80,81,82,83,84,85,88

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

%H G. C. Greubel, <a href="/A047602/b047602.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).

%F a(n) = floor((8/7)*floor(7*(n-1)/6)). - _Bruno Berselli_, May 03 2016

%F From _Chai Wah Wu_, May 29 2016: (Start)

%F a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

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

%F From _Wesley Ivan Hurt_, Jun 15 2016: (Start)

%F a(n) = (24*n-39-3*cos(n*Pi)-4*sqrt(3)*cos((4*n+1)*Pi/6)-12*sin((1-2*n)*Pi/6))/18.

%F a(6k) = 8k-3, a(6k-1) = 8k-4, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)

%F Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*Pi/16 + 7*log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16. - _Amiram Eldar_, Dec 26 2021

%p A047602:=n->floor((8/7)*floor(7*(n-1)/6)): seq(A047602(n), n=1..100); # _Wesley Ivan Hurt_, May 29 2016

%t Table[Floor[(8/7) Floor[7 (n - 1) / 6]], {n, 80}] (* _Vincenzo Librandi_, May 04 2016 *)

%t LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 8}, 50] (* _G. C. Greubel_, May 29 2016 *)

%o (Magma) [n: n in [0..150] | n mod 8 in [0..5]]; // _Vincenzo Librandi_, May 04 2016

%Y Cf. A047420, A047549.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_