A047512 - OEIS

%I #17 Sep 08 2022 08:44:57

%S 1,2,4,6,7,9,10,12,14,15,17,18,20,22,23,25,26,28,30,31,33,34,36,38,39,

%T 41,42,44,46,47,49,50,52,54,55,57,58,60,62,63,65,66,68,70,71,73,74,76,

%U 78,79,81,82,84,86,87,89,90,92,94,95,97,98,100,102,103

%N Numbers that are congruent to {1, 2, 4, 6, 7} 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 From _Chai Wah Wu_, May 30 2016: (Start)

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

%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6. (End)

%F From _Wesley Ivan Hurt_, Jul 28 2016: (Start)

%F a(n) = a(n-5) + 8 for n > 5.

%F a(n) = (40*n - 20 + 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-1, a(5k-1) = 8k-2, a(5k-2) = 8k-4, a(5k-3) = 8k-6, a(5k-4) = 8k-7. (End)

%p A047512:=n->8*floor(n/5)+[(1, 2, 4, 6, 7)][(n mod 5)+1]: seq(A047512(n), n=0..100); # _Wesley Ivan Hurt_, Jul 28 2016

%t Select[Range[0, 100], MemberQ[{1, 2, 4, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 28 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [1, 2, 4, 6, 7]]; // _Wesley Ivan Hurt_, Jul 28 2016

%o (PARI) a(n)=[-1, 1, 2, 4, 6][n%5+1] + n\5*8 \\ _Charles R Greathouse IV_, Jul 29 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_