A047327 Numbers that are congruent to {3, 5, 6} mod 7.

3, 5, 6, 10, 12, 13, 17, 19, 20, 24, 26, 27, 31, 33, 34, 38, 40, 41, 45, 47, 48, 52, 54, 55, 59, 61, 62, 66, 68, 69, 73, 75, 76, 80, 82, 83, 87, 89, 90, 94, 96, 97, 101, 103, 104, 108, 110, 111, 115, 117, 118, 122, 124, 125, 129, 131, 132, 136, 138, 139, 143

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Also, numbers k such that (k^3+1)/7 is a nonnegative integer. - Bruno Berselli, Jan 16 2016

Links

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

Programs

Magma

[n : n in [0..150] | n mod 7 in [3, 5, 6]]; // Wesley Ivan Hurt, Jun 07 2016

Maple

A047327:=n->(21*n-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047327(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Select[Range[0, 150], MemberQ[{3, 5, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 07 2016 *)

Formula

G.f.: x*(3+2*x+x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 07 2016: (Start)

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

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

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