A047306 Numbers that are congruent to {0, 2, 3, 4, 5, 6} mod 7.

0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A016993. - Michel Marcus, Sep 10 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Cf. A016993.

Programs

Magma

[n: n in [0..100] | n mod 7 in [0] cat [2..6]]; // Vincenzo Librandi, Oct 22 2014

Maple

A047306:=n->n+floor((n-2)/6): seq(A047306(n), n=1..100); # Wesley Ivan Hurt, Sep 10 2015

Mathematica

Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 5, 6}, Mod[#, 7]] &] (* Vincenzo Librandi, Oct 22 2014 *)
LinearRecurrence[{1,0,0,0,0,1,-1},{0,2,3,4,5,6,7},70] (* Harvey P. Dale, May 28 2018 *)

PARI

concat(0, Vec(x^2*(2+x+x^2+x^3+x^4+x^5)/((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2) + O(x^30))) \\ Michel Marcus, Oct 22 2014

Formula

G.f.: x^2*(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 10 2015: (Start)

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

a(n) = n + floor((n-2)/6). (End)

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

a(n) = (42*n-27+3*cos(n*Pi)-12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/36.

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

Extensions

More terms from Michel Marcus, Oct 22 2014