A131533 -id:A131533 - cp's OEIS frontend

A153990 Period 6: repeat [1, 2, 5, 4, 7, 8].

1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2, 5, 4, 7, 8, 1, 2

Offset: 0

Paul Curtz, Jan 04 2009

Shares digits with other 6-periodic sequences, see the list in A153130.

Also the decimal expansion of the constant 13942/111111. [R. J. Mathar, Jan 23 2009]

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A131533, A141425, A153130, A154811.

&cat[[1, 2, 5, 4, 7, 8]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

A153990:=n->(27-cos(n*Pi)-8*sqrt(3)*cos((1-4*n)*Pi/6)-16*sin((1+2*n)*Pi/6))/6: seq(A153990(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016

Flatten[Table[{1, 2, 5, 4, 7, 8}, {20}]] (* Wesley Ivan Hurt, Jun 17 2016 *)
PadRight[{},120,{1,2,5,4,7,8}] (* Harvey P. Dale, Nov 08 2017 *)

a(n) - A141425(n) = A131533(n+2).
a(6n+0) + a(6n+5) = a(6n+1) + a(6n+4) = a(6n+2) + a(6n+3) = 9.
G.f.: (1+2*x+5*x^2+4*x^3+7*x^4+8*x^5)/((1-x)*(1+x)*(1+x+x^2)*(x^2-x+1)). [R. J. Mathar, Jan 23 2009]
From Wesley Ivan Hurt, Jun 17 2016: (Start)
a(n) = (27-cos(n*Pi)-8*sqrt(3)*cos((1-4*n)*Pi/6)-16*sin((1+2*n)*Pi/6))/6.
a(n) = a(n-6) for n>5. (End)

Edited by R. J. Mathar, Jan 23 2009

A245477 Period 6: repeat [1, 1, 1, 1, 1, 2].

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset: 0

Hailey R. Olafson, Jul 23 2014

First differences of A047368. The first differences of this sequence are in A131533. - Wesley Ivan Hurt, Jul 24 2014

Binomial Transform of a(n) gives: 1, 2, 4, 8, 16, 33, 70, 149, 312, 638, 1276, 2511, ... - Wesley Ivan Hurt, Aug 13 2014

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A024643, A047368, A097325, A130782, A131534, A172051, A177702, A177704, A177706.

[Floor((n+1)*7/6) - Floor((n)*7/6) : n in [0..100]]; // Wesley Ivan Hurt, Aug 06 2014

A:= n -> piecewise(n mod 6 = 5, 2, 1);
seq(A(n), n=0..100); # Robert Israel, Jul 23 2014

Table[2 - Sign[Mod[n + 1, 6]], {n, 0, 100}] (* Wesley Ivan Hurt, Jul 24 2014 *)
PadRight[{},120,{1,1,1,1,1,2}] (* Harvey P. Dale, Jun 02 2016 *)

a(n) = 7*(n+1)\6 - 7*n\6; \\ Michel Marcus, Jul 23 2014

[floor((n+1)*7/6) - floor((n)*7/6) for n in [0..200]]

a(n) = floor((n+1)*7/6) - floor((n)*7/6).
G.f.: 1/(1-x) + x^5/(1-x^6). - Robert Israel, Jul 23 2014
From Wesley Ivan Hurt, Jul 24 2014, Aug 06-29 2014: (Start)
  a(n) = 2 - sign((n+1) mod 6).
  a(n) = 3 - 2^sign((n+1) mod 6).
  a(n) = A172051(n) + 1.
  a(2n) = 1, a(2n+1) = A177702(n).
  Sum_{i=0..n-2} a(i) = A047368(n), n>0.
  a(n) = 1 + mod(n, 1 + mod(n-1, 3)).
  a(n) = 1 + binomial(mod(5n + 10, 6), 5). (End)
From Wesley Ivan Hurt, Jun 23 2016: (Start)
a(n) = a(n-6) for n>5.
a(n) = (7 - cos(n*Pi) + cos(n*Pi/3) - cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/6. (End)

cp's OEIS Frontend

A153990 Period 6: repeat [1, 2, 5, 4, 7, 8].

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