A047391 Numbers that are congruent to {1, 3, 5} mod 7.

1, 3, 5, 8, 10, 12, 15, 17, 19, 22, 24, 26, 29, 31, 33, 36, 38, 40, 43, 45, 47, 50, 52, 54, 57, 59, 61, 64, 66, 68, 71, 73, 75, 78, 80, 82, 85, 87, 89, 92, 94, 96, 99, 101, 103, 106, 108, 110, 113, 115, 117, 120, 122, 124, 127, 129, 131, 134, 136, 138, 141

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A049347.

Programs

Magma

[n: n in [1..122] | n mod 7 in [1, 3, 5]]; // Bruno Berselli, Mar 25 2011

Maple

A047391:=n->(21*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9: seq(A047391(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 3, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 13 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 5, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

Formula

From Bruno Berselli, Mar 25 2011: (Start)

G.f.: x*(1+2*x+2*x^2+2*x^3)/((1-x)^2*(1+x+x^2)).

a(n) = 7*floor((n-1)/3)+2*(n-1 mod 3)+1.

a(n) = (1/3)*(7*n-5-A049347(n)). (End)

From Wesley Ivan Hurt, Jun 13 2016: (Start)

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

a(n) = (21*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9.

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

a(n) = n - 1 + floor((4n-1)/3). - Wesley Ivan Hurt, Dec 27 2016