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%I #20 Sep 08 2022 08:44:57
%S 0,1,3,5,6,8,9,11,13,14,16,17,19,21,22,24,25,27,29,30,32,33,35,37,38,
%T 40,41,43,45,46,48,49,51,53,54,56,57,59,61,62,64,65,67,69,70,72,73,75,
%U 77,78,80,81,83,85,86,88,89,91,93,94,96,97,99,101,102,104
%N Numbers that are congruent to {0, 1, 3, 5, 6} mod 8.
%H Vincenzo Librandi, <a href="/A047446/b047446.txt">Table of n, a(n) for n = 1..1000</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) = floor((8n-7)/5). [_Gary Detlefs_, Mar 07 2010]
%F G.f.: x^2*(1+2*x+2*x^2+x^3+2*x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F From _Wesley Ivan Hurt_, Jul 31 2016: (Start)
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.
%F a(n) = (40*n - 45 + 3*(n mod 5) - 2*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) - 2*((n+4) mod 5))/25.
%F a(5k) = 8k-2, a(5k-1) = 8k-3, a(5k-2) = 8k-5, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)
%p seq(floor((8*n-7)/5), n=1..57); # _Gary Detlefs_, Mar 07 2010
%t Select[Range[0, 100], MemberQ[{0, 1, 3, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 31 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3, 5, 6]]; // _Wesley Ivan Hurt_, Jul 31 2016
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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