|
%I #18 Sep 08 2022 08:44:57
%S 1,2,3,4,5,8,9,10,11,12,15,16,17,18,19,22,23,24,25,26,29,30,31,32,33,
%T 36,37,38,39,40,43,44,45,46,47,50,51,52,53,54,57,58,59,60,61,64,65,66,
%U 67,68,71,72,73,74,75,78,79,80,81,82,85,86,87,88,89,92
%N Numbers that are congruent to {1, 2, 3, 4, 5} mod 7.
%H Vincenzo Librandi, <a href="/A047369/b047369.txt">Table of n, a(n) for n = 1..1000</a>
%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+x+x^2+x^3+x^4+2*x^5) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F From _Wesley Ivan Hurt_, Aug 08 2016: (Start)
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 7 for n > 5.
%F a(n) = n + 2*floor((n-1)/5), a(n) = 7*n/5 - 2*(1 + ((n+4) mod 5))/5.
%F a(5*k) = 7*k-2, a(5*k-1) = 7*k-3, a(5*k-2) = 7*k-4, a(5*k-3) = 7*k-5, a(5*k-4) = 7*k-6. (End)
%p A047369:=n->7*floor(n/5)+[(1, 2, 3, 4, 5)][(n mod 5)+1]: seq(A047369(n), n=0..100); # _Wesley Ivan Hurt_, Aug 08 2016
%t Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Aug 08 2016 *)
%t LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 5, 8}, 100] (* _Vincenzo Librandi_, Aug 08 2016 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [1..5]]; // _Wesley Ivan Hurt_, Aug 08 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
|
