A133875 - OEIS

%I #17 Sep 08 2022 08:45:32

%S 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,0,0,0,0,0,1,1,1,1,1,2,2,2,2,

%T 2,3,3,3,3,3,4,4,4,4,4,0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,

%U 4,4,0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,0,0,0,0,0,1,1,1,1,1

%N n modulo 5 repeated 5 times.

%C Periodic with length 5^2 = 25.

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1).

%F a(n) = (1 + floor(n/5)) mod 5.

%F a(n) = A010874(A002266(n+5)).

%F a(n) = 1 + floor(n/5) - 5*floor((n+5)/25).

%F a(n) = (((n+5) mod 25) - (n mod 5)) / 5.

%F a(n) = ((n + 5 - (n mod 5)) / 5) mod 5.

%F a(n) = A010874((n + 5 - A010874(n))/5).

%F a(n) = binomial(n+5, n) mod 5 = binomial(n+5, 5) mod 5.

%F a(n) = +a(n-1) -a(n-5) +a(n-6) -a(n-10) +a(n-11) -a(n-15) +a(n-16) -a(n-20) +a(n-21). - R. J. Mathar, Sep 03 2011

%F G.f.: ( 1+2*x^5+3*x^10+4*x^15 ) / ( (1-x)*(x^20+x^15+x^10+x^5+1) ). - _R. J. Mathar_, Sep 03 2011

%p A133875:=n->((1+floor(n/5)) mod 5); seq(A133875(n), n=0..100); # _Wesley Ivan Hurt_, Jun 06 2014

%t Table[Mod[1 + Floor[n/5], 5], {n, 0, 100}] (* _Wesley Ivan Hurt_, Jun 06 2014 *)

%t LinearRecurrence[{1,0,0,0,-1,1,0,0,0,-1,1,0,0,0,-1,1,0,0,0,-1,1},{1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,0},120] (* _Harvey P. Dale_, Dec 14 2017 *)

%o (Magma) [(1 + Floor(n/5)) mod 5 : n in [0..50]]; // _Wesley Ivan Hurt_, Jun 06 2014

%Y Cf. A133620-A133625, A133630, A038509, A133634-A133636.

%Y Cf. A133885, A133880, A133890, A133900, A133910.

%K nonn,easy,less

%O 0,6

%A _Hieronymus Fischer_, Oct 10 2007