A047310 Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 7.

0, 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A017005. - Michel Marcus, Sep 08 2015

Links

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

Crossrefs

Cf. A017005 (7n+2).

Programs

Magma

[n+Floor((n-3)/6): n in [1..100]]; // Wesley Ivan Hurt, Sep 08 2015

Magma

[n: n in [0..100] | n mod 7 in [0,1,3,4,5,6]]; // Vincenzo Librandi, Sep 10 2015

Maple

A047310:=n->n+floor((n-3)/6): seq(A047310(n), n=1..100); # Wesley Ivan Hurt, Sep 08 2015

Mathematica

Table[n+Floor[(n-3)/6], {n, 100}] (* Wesley Ivan Hurt, Sep 08 2015 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7}, 70] (* Vincenzo Librandi, Sep 10 2015 *)
Select[Range[0,100],MemberQ[{0,1,3,4,5,6},Mod[#,7]]&] (* Harvey P. Dale, Dec 02 2024 *)

Formula

G.f.: x^2*(1+2*x+x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Sep 08 2015: (Start)

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

a(n) = n + floor((n-3)/6). (End)

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

a(n) = (42*n-33-3*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-4, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)

Extensions

More terms from Vincenzo Librandi, Sep 10 2015