A047343 Numbers that are congruent to {1, 3, 4} mod 7.

1, 3, 4, 8, 10, 11, 15, 17, 18, 22, 24, 25, 29, 31, 32, 36, 38, 39, 43, 45, 46, 50, 52, 53, 57, 59, 60, 64, 66, 67, 71, 73, 74, 78, 80, 81, 85, 87, 88, 92, 94, 95, 99, 101, 102, 106, 108, 109, 113, 115, 116, 120, 122, 123, 127, 129, 130, 134, 136, 137, 141

Offset

1,2

Comments

Also, numbers n such that kronecker(n+2, 7) = -1. - M. F. Hasler, Mar 15 2013

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(1+2*x+x^2+3*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 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-18-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047343:=n->(21*n-18-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047343(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Flatten[Table[{7n + 1, 7n + 3, 7n + 4}, {n, 0, 19}]] (* Alonso del Arte, Mar 15 2013 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 4, 8}, 90] (* Harvey P. Dale, Aug 07 2021 *)

Prog

(PARI) A047343(n)=n\3*7+[-3, 1, 3][n%3+1] \\ M. F. Hasler, Mar 15 2013
(PARI) for(k=1, 200, kronecker(k+2, 7)==-1 & print1(k", ")) \\ For illustrative purpose of the comment. - M. F. Hasler, Mar 15 2013
(Magma) [n : n in [0..150] | n mod 7 in [1, 3, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A239976 A191193 A327185 * A155730 A005047 A083317

Adjacent sequences: A047340 A047341 A047342 * A047344 A047345 A047346

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved