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%I A047603 #18 Sep 08 2022 08:44:57
%S A047603 1,2,3,4,5,9,10,11,12,13,17,18,19,20,21,25,26,27,28,29,33,34,35,36,37,
%T A047603 41,42,43,44,45,49,50,51,52,53,57,58,59,60,61,65,66,67,68,69,73,74,75,
%U A047603 76,77,81,82,83,84,85,89,90,91,92,93,97,98,99,100,101
%N A047603 Numbers that are congruent to {1, 2, 3, 4, 5} mod 8.
%H A047603 Vincenzo Librandi, <a href="/A047603/b047603.txt">Table of n, a(n) for n = 1..1000</a>
%H A047603 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A047603 From _Chai Wah Wu_, Jun 10 2016: (Start)
%F A047603 a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.
%F A047603 G.f.: x*(3*x^5 + x^4 + x^3 + x^2 + x + 1)/(x^6 - x^5 - x + 1). (End)
%F A047603 From _Wesley Ivan Hurt_, Jul 28 2016: (Start)
%F A047603 a(n) = a(n-5) + 8 for n>5.
%F A047603 a(n) = (40*n - 45 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) - 12*((n+4) mod 5))/25.
%F A047603 a(5k) = 8k-3, a(5k-1) = 8k-4, a(5k-2) = 8k-5, a(5k-3) = 8k-6, a(5k-4) = 8k-7. (End)
%F A047603 a(n) = n + 3*floor((n-1)/5). - _Wesley Ivan Hurt_, Aug 08 2016
%p A047603 A047603:=n->8*floor(n/5)+[(1, 2, 3, 4, 5)][(n mod 5)+1]: seq(A047603(n), n=0..100); # _Wesley Ivan Hurt_, Jul 28 2016
%t A047603 Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 28 2016 *)
%t A047603 LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 5, 9}, 100] (* _Vincenzo Librandi_, Aug 08 2016 *)
%o A047603 (Magma) [n : n in [0..150] | n mod 8 in [1..5]]; // _Wesley Ivan Hurt_, Jul 28 2016
%K A047603 nonn,easy
%O A047603 1,2
%A A047603 _N. J. A. Sloane_

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