A047360 Numbers that are congruent to {1, 2, 3} mod 7.

1, 2, 3, 8, 9, 10, 15, 16, 17, 22, 23, 24, 29, 30, 31, 36, 37, 38, 43, 44, 45, 50, 51, 52, 57, 58, 59, 64, 65, 66, 71, 72, 73, 78, 79, 80, 85, 86, 87, 92, 93, 94, 99, 100, 101, 106, 107, 108, 113, 114, 115, 120, 121, 122, 127, 128, 129, 134, 135, 136, 141

Offset

1,2

Links

Table of n, a(n) for n=1..61.

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

Formula

a(n) = 7*floor(n/3)+(n mod 3)+1, with offset 0. - Gary Detlefs, Mar 09 2010

G.f.: x*(1+x+x^2+4*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

a(n) = 4*floor((n-1)/3)+n. - Gary Detlefs, Dec 22 2011

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (21*n-24-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

seq(7*floor(n/3)+(n mod 3)+1, n=0..52); # Gary Detlefs, Mar 09 2010

Mathematica

Select[Range[0, 200], Mod[#, 7] == 1 || Mod[#, 7] == 2 || Mod[#, 7] == 3 &] (* Vladimir Joseph Stephan Orlovsky, Jul 10 2011 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [1..3]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A169868 A363088 A191159 * A004825 A272830 A028821

Adjacent sequences: A047357 A047358 A047359 * A047361 A047362 A047363

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved