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

1,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A049347.

Sequence in context: A342871 A191160 A189929 * A184655 A090846 A195170

Adjacent sequences: A047388 A047389 A047390 * A047392 A047393 A047394

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved