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

1,3

Comments

Complement of A017005. - Michel Marcus, Sep 08 2015

Links

Table of n, a(n) for n=1..68.

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

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)

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 *)

Prog

(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

Crossrefs

Cf. A017005 (7n+2).

Sequence in context: A116587 A057903 A247833 * A184530 A304804 A359776

Adjacent sequences: A047307 A047308 A047309 * A047311 A047312 A047313

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Sep 10 2015

Status

approved