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A047310 Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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 A077656

Adjacent sequences:  A047307 A047308 A047309 * A047311 A047312 A047313

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vincenzo Librandi, Sep 10 2015

STATUS

approved

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Last modified June 22 19:28 EDT 2021. Contains 345388 sequences. (Running on oeis4.)