|
%I #19 Sep 08 2022 08:44:57
%S 1,2,3,4,5,7,9,10,11,12,13,15,17,18,19,20,21,23,25,26,27,28,29,31,33,
%T 34,35,36,37,39,41,42,43,44,45,47,49,50,51,52,53,55,57,58,59,60,61,63,
%U 65,66,67,68,69,71,73,74,75,76,77,79,81,82,83,84,85,87
%N Numbers that are congruent to {1, 2, 3, 4, 5, 7} mod 8.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-1).
%F G.f.: x*(1+x^2+x^4+x^5) / ( (x^2-x+1)*(1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Nov 06 2015
%F From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
%F a(n) = (12*n-9+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9.
%F a(6k) = 8k-1, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2-sqrt(2))/4. - _Amiram Eldar_, Dec 28 2021
%p A047504:=n->(12*n-9+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9: seq(A047504(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)
%o (Magma) [n : n in [0..100] | n mod 8 in [1, 2, 3, 4, 5, 7]]; // _Wesley Ivan Hurt_, Jun 16 2016
%Y Cf. A047451 (complement), A047422, A047519.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
|
