A047427 - OEIS

%I #19 Sep 08 2022 08:44:57

%S 1,3,4,5,6,9,11,12,13,14,17,19,20,21,22,25,27,28,29,30,33,35,36,37,38,

%T 41,43,44,45,46,49,51,52,53,54,57,59,60,61,62,65,67,68,69,70,73,75,76,

%U 77,78,81,83,84,85,86,89,91,92,93,94,97,99,100,101,102

%N Numbers that are congruent to {1, 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 G.f.: x*(1+2*x+x^2+x^3+x^4+2*x^5) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011

%F From _Wesley Ivan Hurt_, Aug 01 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 - 25 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) - 2*((n+3) mod 5) - 7*((n+4) mod 5))/25.

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

%p A047427:=n->8*floor(n/5)+[(1, 3, 4, 5, 6)][(n mod 5)+1]: seq(A047427(n), n=0..100); # _Wesley Ivan Hurt_, Aug 01 2016

%t Select[Range[0, 100], MemberQ[{1, 3, 4, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Aug 01 2016 *)

%t LinearRecurrence[{1,0,0,0,1,-1},{1,3,4,5,6,9},70] (* _Harvey P. Dale_, Dec 15 2018 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [1, 3, 4, 5, 6]]; // _Wesley Ivan Hurt_, Aug 01 2016

%o (PARI) a(n)=[-2,1,3,4,5][n%5+1] + n\5*8 \\ _Charles R Greathouse IV_, Aug 01 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_