A047318 Numbers that are congruent to {0, 1, 2, 4, 5, 6} mod 7.

0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 82, 83

Offset

1,3

Comments

Complement of A017017. - Michel Marcus, Sep 10 2015

Links

Table of n, a(n) for n=1..72.

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

Formula

G.f.: x^2*(1+x+2*x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011

From Wesley Ivan Hurt, Sep 10 2015: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = n + floor((n-4)/6). (End)

From Wesley Ivan Hurt, Jun 15 2016: (Start)

a(n) = (42*n-39+3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)+12*sin((1-2*n)*Pi/6))/36.

a(6k) = 7k-1, a(6k-1) = 7k-2, a(6k-2) = 7k-3, a(6k-3) = 7k-5, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)

Maple

for n from 0 to 200 do if n mod 7 <> 3 then printf(`%d, `, n) fi: od:
A047318:=n->n+floor((n-4)/6): seq(A047318(n), n=1..100); # Wesley Ivan Hurt, Sep 10 2015

Mathematica

Table[n+Floor[(n-4)/6], {n, 100}] (* Wesley Ivan Hurt, Sep 10 2015 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6, 7}, 100] (* Vincenzo Librandi, Sep 11 2015 *)
DeleteCases[Range[0, 100], _?(Mod[#, 7]==3&)] (* Harvey P. Dale, May 07 2016 *)

Prog

(Magma) [n+Floor((n-4)/6) : n in [1..100]]; // Wesley Ivan Hurt, Sep 10 2015
(Magma) [n : n in [0..140] | n mod 7 in [0, 1, 2, 4, 5, 6]]; // Vincenzo Librandi, Sep 11 2015

Crossrefs

Cf. A017017.

Sequence in context: A294662 A183301 A308065 * A057904 A188397 A027925

Adjacent sequences: A047315 A047316 A047317 * A047319 A047320 A047321

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Feb 19 2001

Status

approved