A047423 - OEIS

%I #18 Sep 08 2022 08:44:57

%S 2,3,4,5,6,10,11,12,13,14,18,19,20,21,22,26,27,28,29,30,34,35,36,37,

%T 38,42,43,44,45,46,50,51,52,53,54,58,59,60,61,62,66,67,68,69,70,74,75,

%U 76,77,78,82,83,84,85,86,90,91,92,93,94,98,99,100,101,102

%N Numbers that are congruent to {2, 3, 4, 5, 6} mod 8.

%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+1) = 3*floor(n/5) + n + 2. - _Gary Detlefs_, Mar 12 2010

%F G.f.: x*(1+x)*(2*x^4-x^3+2*x^2-x+2) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 05 2011

%F From _Wesley Ivan Hurt_, Aug 03 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) = (8*n + 2 - 3*((n+4) mod 5))/5.

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

%p A047423:=n->8*floor(n/5)+[(2, 3, 4, 5, 6)][(n mod 5)+1]: seq(A047423(n), n=0..100); # _Wesley Ivan Hurt_, Aug 03 2016

%t Select[Range[0, 100], MemberQ[{2, 3, 4, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Aug 03 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [2..6]]; // _Wesley Ivan Hurt_, Aug 03 2016

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_